陕西英语往年高考试题文档含答案

西安高考英语试题及答案一、听力部分（共20分）1. 根据所听对话，选择正确的图片。

（每题1分，共5分）A. 一位老师正在讲课。

B. 两个学生在图书馆讨论。

C. 一家人在公园野餐。

D. 一位医生在给病人看病。

E. 一位游客在询问路线。

答案：B, A, C, D, E2. 根据所听短文，回答以下问题。

（每题2分，共10分）问题一：What is the main topic of the passage?答案：The main topic is about the importance of environmental protection.问题二：What does the speaker suggest people should do to protect the environment?答案：The speaker suggests people should reduce the use of plastic bags and recycle more.问题三：What are the negative effects of pollution mentioned in the passage?答案：The negative effects include air pollution causing health problems and water pollution affecting wildlife.问题四：What is the role of the government in environmental protection?答案：The government's role is to enact laws and regulations to control pollution and promote green energy.问题五：What is the speaker's attitude towards the future of environmental protection?答案：The speaker is optimistic about the future,believing that with collective efforts, the environment can be improved.3. 根据所听对话，填写缺失的信息。

高中英语学习材料madeofjingetieji第一部分：英语知识运用（共四节，满分55分）第一节语音知识（共5小题；每小题1分，满分5分）从每小题的A、B、C、D四个选项中，找出其划线部分与所给单词的划线部分读音相同的选项，并在答题卡上将该选项涂黑。

1. openA. becomeB. acrossC. lonelyD. balcony2. teacherA. greatB. heavyC. ideaD. disease3. physicsA. pleasureB. musicC. sureD. increase第二节情景对话（共5小题；每小题1分，满分5分）根据对话情境和内容，从对话后所给的选项中选出能填入每一空白处的最佳选项，并在答题卡上将该选项涂黑。

选项中有两个为多余选项。

Linda: Hello, George. 6George: Hi, Linda. I’m reading a tourist guide to Europe.Linda: 7George: Yes, i’m looking to such a trip. Hey, have you ever been there?Linda: Yes. I’ve actually visited my countries in Europe; France, Germany, Italy and Austria, for example.George: 8 And how long did you stay?Linda: Two years ago. For over one month.George: Did you like it?Linda: 9 There are many ancient churches and castles. It’s the best trip I’ve ever taken.George: Sounds great. 10Linda: Good idea. You won’t regret it.A: Of course.B: Not exactly.C: What are you doing?D: When did you go there?E: Do you plan to move to Europe?F: Are you thinking of visiting Europe some day?G: I decide to make a trip next October on my annual leave.第三节语法和词汇知识（共15小题；每小题1分，满分15分）从每小题的A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该选项涂黑。

第一部分：英语知识运用（共四节，满分55分）第一节语音知识（共5小题；每小题1分，满分5分）从每小题的A、B、C、D四个选项中，找出其划线部分与所给单词的划线部分读音相同的选项，并在答题卡上将该选项涂黑。

1. stomachA. technologyB. exchangeC. chairD. church2. uncleA. concertB. strangeC. blanketD. autumn3. exactA. excellentB. exampleC. exerciseD. expensive4. tableA. cottageB. basketC. wakeD. family5. doubleA. soulB. groupC. pronounceD. couple【答案】1.A2.C3.B4.C5.D5.double和couple里面的字母ou都是读/ ? /，soul里面的字母ou读/??/，group里面的字母ou读/u：/，pronounce里面的字母ou读/au/,选D。

【考点定位】考查单词辨音第二节情景对话（共5小题；每小题1分，满分5分）根据对话情境和内容，从对话后所给的选项中选出能填入每一空白处的最佳选项，并在答题卡上将该选项涂黑。

选项中有两个为多余选项。

Doctor: Good morning, Sir. 6Johnson :Yes, doctor. I'm always tired but when I go to bed I can't sleep.Doctor: 7Johnson : Since I started my new job two months ago.Doctor : What is your job ?Johnson : I’m in advertising. 8Doctor : It depends. How many hours do you work?Johnson: About 80 hours a weekDoctor: 9 . Do you often take exercise?Johnson: Not very often. 10 .Doctor; Well, you do need to find some time. Try to work less, or look for a more stress-free job.A. That's a lot!B. I like my job.C. Does it matter?D. How can I help you?E. I don't have the time.F. What time do you usually go to bed?G.. How long have you had this problem?【答案】6.D7.G8.C9.A10.E10.根据上句：Not very often，可知这里是：我没有时间（锻炼）。

2024年陕西高考英语试题及答案第一部分听力（共两节, 满分30分）第一节（共5小题; 每小题1. 5分, 满分7. 5分）听下面5段对话。

每段对话后有一个小题, 从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后, 你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. Where are the speakers going?A. A new restaurant.B. A convenience store.C. Their office.2. When is the class presentation according to Vicky?A. On Thursday.B. On Wednesday.C. On Tuesday.3. Why does the woman make the call?A. To check the price.B. To make an apology.C. To cancel her order.4. What is the probable relationship between the speakers?A. Husband and wife.B. Boss and employee.C. Salesperson and customer.5. What are the speakers mainly talking about?A. Their move to a new place.B. Tom's friends at school.C. A sports center. 第二节（共15小题; 每小题1. 5分, 满分22. 5分）听下面5段对话或独白。

每段对话或独白后有几个小题, 从题中所给的A、B、C三个选项中选出最佳选项。

听每段对话或独白前, 你将有时间阅读各个小题, 每小题5秒钟; 听完后, 各小题将给出5秒钟的作答时间。

绝密★启封并使用完毕前2010年普通高等学校招生全国统一考试(陕西卷)英语第一部分英语知识运用(共四节,满分55分)第一节语音知识(共5小题,每小题1分,满分5分)从每小题的A、B、C、D四个选项中,找出所给单词的正确读音,并在答题卡上将该选项涂黑.1.taste (A)A./terst/B./t st/C.D./ta:st/2. touch ( C)A. B. C. D.3. rely ( D)A. B. C. D.4. loss (B)A. B. C. D.5. agriculrure (A)A. B. C. D.第二节情景对话(共5小题,每小题1分,满分5分)根据对话情景和内容,从对话后所给的选项中选出能填入每一空白处的最佳选项,并在答题卡上将该选项涂黑.选项中有两个为多余选项Jerry: Hi , Mike. Look like you’ve got some sun .Mike: I guess so. I spent the weekend on the beach.Jerry: Really? That sounds exciting. __6__ ( C )Mike:At my friend’s house .He invited me to stay there for as long as I wanted .Jerry: __7__ (G )Mike: Oh, I have a paper to work on.Jerry: _8__ I mean besides lying out in the sun. ( E )Mike: I play some volleyball . I never realized how hard it is to run on sand.Jerry: _9__ Did you go swimming? ( B )Mike: I intended to . __10__So I just went fishing. ( F )Jerry: All sounds so relaxing.A. What a pity!B.It must be cool.C.Where did you stay ?D. But how did you get there ?E.So what else did you do out there ?F.But the water wasn’t warm enoughG..Then why not stay there for a longer time?第三节语法和词汇知识(共15小题,每小题1分,满分15分)从每小题的A、B、C、D四个选项中,选出可以填入空白处的最佳选项,并在答题卡上将该选项涂黑.11.The old temple _______ roof was damaged in storm is now under repair. ( D )A. whereB. whichC. itsD. whose12. The cost of renting a house in central Xi’an is higher than ____ in any other area of the city.A.thatB. thisC. itD. one (A )13. –What’s the noise ? It sounds as if it comes from upstairs.--______ .It must be the window-cleaner working , next door. (D)A.I’m not sureB. I hope notC.I’d rather notD. I don’t think so14. You look well . The air and the sea foods in Sanya must _____ you , I suppose. (A )A.agree withB.agree toC. agree onD. agree about15.If we ___ the other road ,we might have arrived here in time for the meeting. (B)A.takeB.had takenC.tookD. have taken16._____ from the top of the tower ,the south foot of the mountain is a sea of trees . (A )A.SeenB.SeeingC.Have seenD. To see17.John opened the door . There _____ he had never seen before. (D)A.a girl did standB. a girl stoodC.did a girl standD. stood a girl18.It never occurred to me _____ you could succeed in persuading him to change his mind. (D)A.whichB.whatC.thatD. if19. His first book next month is based on a true story. (B)A. publishedB. to be publishedC. to publishD. being published20. John thinks it won’t be long he is ready for his new job. (C)A. whenB. afterC. beforeD. since21. I have to see the doctor because I a lot lately. (A)A. have been coughingB. had coughedC. coughedD. cough22. Studies show that people are more to suffer from back problems if they always sit before computer screens for long hours. (A)A. likelyB. possibleC. probableD. sure23. May I take this book out of the reading room?No,you . You read it in here. (D)A. mightn’tB. won’tC. need’tD. mustn’t24. It is reported that many a new house at present in the disater area. (D)A. are being builtB. were being builtC. was being builtD. is being built25. What a fine day! Shall we go picnicking?. But we need to be home before six o’clock for the football match.. (C)A. Have a nice time.B. Pardon meC. That’s greatD. You are right第四节完形填空（共20小题，每小题1.5分，满分30分）I used to live selfishly, I should admit. But one moment changed me.I was on my lunch break and had 26 the office to ger something to eat . On the way, I 27 aBusker(街头艺人)，with a hat in front of him. I had some 28 in my pocker, but I would not give them to him, thinking to myself he would 29 use the money to feed his addiction to drugs or alcohol. He 30 like that type-young and ragged. 31 what was I going to spend the money on ? Only to feed my addiction to Coca-Cola orchocolate! I then 32 I had no right to place myself above 33 just because he was busking.I 34 and dropped all the coins into his 35, and he smiled at me, I watched for a while. As 36 as it sounds, I expected something more to come from that moment—a feeling of 37 or satifaction, for example. But nothing happened 38 , I walked off. “It proved to be a waste of 39 ,”I thought.On my way home at the end of the 40, I saw the busker again and he was 41 . I watched him pick up the hat and walk 42 a cafe counter. There he poured the 43 contents into a tin collecting 44 an earthquake fund-raising(募捐) event. He was busking for charity(慈善)！Now I donate any 45 I have to charity tins and enjoy the feeling of giving.26. A. left B. cleaned C. prepared D.searched (A)27. A. led B. chose C. saw D. fooled (C)28. A. chocolates B. coins C. tins D. drugs (B)29. A. almost B. only C. rather D. still (B)30. A. acted B. looked C. sounded D.smelt (B)31. A. Though B. For C. Therefor D. But (D)32. A. declared B. realized C. expected D. guessed (B)33. A. it B. all C. him D. them (C)34. A. waited B. followed C. stopped D. arrived (C)35. A. rag B. hat C. pocket D. counter (B)36. A. selfish B. awkward C. innocent D. special (A)37. A. happeiness B. sadness C. love D. hate (A)38. A. Disappointedly B. Unfortunately C. Coincidentally D. Comfortably (A)39. A. words B. effort C. space D. money (D)40. A. moment B. day C. break D. event (B)41. A. walking around B. passing by C. packing up D. running off (C)42. A. around B. in C. behind D. to (D)43.A. chief B. basic C. actual D. total 【D】44.A.by B. for C. on D. with 【B】45.A.work B. time C. energy D.change 【D】第二部分阅读理解（共两节，满分40分）第一节（共15小题，每小题2分，满分30分）阅读下列四篇短文，从每小题后所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该选项涂黑。

陕西二卷英语试题及答案一、听力理解（共20分）1. What did the man do yesterday?A. He went to a concert.B. He visited his uncle.C. He stayed at home.2. Where are the speakers now?A. In a library.B. In a restaurant.C. In a bookstore.3. What time does the train leave?A. At 6:00 pm.B. At 7:00 pm.C. At 8:00 pm.4. Why is the woman upset?A. She lost her job.B. She missed her bus.C. She broke her phone.5. What does the man suggest doing?A. Going to the cinema.B. Going to the park.C. Going to the beach.二、阅读理解（共30分）Passage 16. What is the main idea of the passage?A. The importance of physical exercise.B. The benefits of outdoor activities.C. The impact of technology on daily life.7. According to the article, which of the following is a negative effect of technology?A. It makes people more social.B. It reduces physical activity.C. It improves mental health.8. What does the author suggest to combat the negative effects of technology?A. Limiting screen time.B. Encouraging outdoor activities.C. Banning technology use.Passage 29. What is the purpose of the text?A. To advertise a new product.B. To announce an upcoming event.C. To provide travel information.10. When is the event scheduled to take place?A. On the 15th of June.B. On the 20th of June.C. On the 25th of June.11. What is included in the event package?A. Accommodation and meals.B. Transportation and tickets.C. Guided tours and souvenirs.12. How can interested individuals register for the event?A. By phone.B. By email.C. In person.三、完形填空（共20分）13. The word "abandoned" in the first paragraph most probably means ______.A. forgottenB. neglectedC. cherished14. What was the main reason for the factory's closure?A. Financial difficulties.B. Environmental regulations.C. Technological advancements.15. How did the local community react to the factory's reopening?A. They were excited.B. They were indifferent.C. They were concerned.四、语法填空（共15分）16. If it ______ (not rain) tomorrow, we will go for a picnic.17. She ______ (be) a teacher for ten years by the time she retires next year.18. The book is worth ______ (read).19. ______ (not make) any noise while you are in the library.20. I ______ (hear) from my brother since last month.五、短文改错（共15分）21. Last week, my family and I went to a beautiful beach for vacation. We had a wonderful time there. The weather was fine and the beach was crowded of people. We played volleyball and swam in the sea. In the evening, we had a delicious dinner at a nearby restaurant. I hope to go back there again in the future.六、书面表达（共20分）22. Write an essay of about 120 words on the topic "The Role of Technology in Education". You should write clearly and coherently, including an introduction, body, and conclusion. (Start your essay with the phrase "In recent years, technology has become an integral part of education...")答案：一、听力理解1-5 CABBA二、阅读理解6-8 CAB9-12 CBAC三、完形填空13-15 BAC四、语法填空16. doesn't rain17. will have been18. reading19. Don't make20. haven't heard五、短文改错21. crowded of people → crowde d with people六、书面表达范文略。

英语陕西英语一、英语知识运用（共三大题，满分50分）（一）语音知识（共5小题，每小题1分，满分5分）从每小题的A B C D四个选项中，找出其划线部分与所给单词的划线部分读音相同的选项，并在答题卡上将该选项涂黑。

1. permi．t AA fistB behindC istandD smile2 . question CA revolutionB exhibitionC suggestionD education3. empty DA toilerB dozenC generalD connect4. social AA preciousB certainC discoveryD decision5. forget BA ordinaryB majorC worldD report(二)语法和词汇知识（共15小题，每小题1分，满分15分）从每小题的A B C D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该选项涂黑。

6. What pity that you couldn’t be there to receive prize! CA a;aB the ; aC a ; theD the;the7. Dr.Smith, together with his wife and daughters , visit Beijing this summer. AA is going toB are going toC was going toD were goingto8.He invited me to a dance after the show Chrismas Eve. BA atB onC inD by9.This is the first time wen a film in the cinema together as a family. DA seeB had seenC sawD have seen10.Jane was asked a lot of questions ,but she didn’t answer of them .BA otherB anyC noneD some11. Gun control is a subject Americans have argued for a long time . CA of whichB with whichC about whichD into which12.I still remember to the Famen Temple and what I saw there . DA to takeB to be takenC takingD being taken13.My parents don’t mind what job I do I am happy . CA even thoughB as soon asC as long asD as though14.—My mother is preparing my favorite dishes .Go with me and have a taste ,okay?-- .And I’ll be glad to meet your parents . BA I think soB I’d love toC I’m sureD I hope so15.A notice was in order to remind the students of the changed lecture time . DA sent upB given upC set upD put up16. He must be helping the old man to water the flowers, ? BA is heB isn’t heC must heD mustn’t he17. The how to booke can be of help to wants to do the job. DA whoB whomeverC no matter whoD whoever18.Little about her own safety ,though she was in great danger herself. AA did Rose careB Rose didi careC Rose does careD does Rose care19.—Have you finished your first paper? D-- .Just half of it .How about you?A.Not at allB.Not likelyC. Not a bitD.Not yet20. Form their ________ on the top of the TV Tower, visitors can have a better view of the city.A. stageB.positionC. conditionD. situation(三)完形填空（共20小题，每小题1.5分，满分30分）阅读下面短文，从短文后面各题的A、B、C、D四个选项中，选出适合填入对应空白处的最佳选项，并在答题卡上将该选项涂黑。

陕西省英语高考历年真题及答案陕西省英语高考历年真题及答案DThe most common problem that worries all of us today is the fear of insecurity. Life has become so competitive that every now and then we are struck (遭遇) by the fear of the unknown. With every new turn of events our self-confidence takes a blow. The biggest challenge before every person today is not to lose confidence in one’s ability.There are several reasons that affect a person’s self-confidence. The most important reason is lack of success. Not being able to succeed affects one’s self-confidence greatly. This is when one begins to doubt his own ability. In many cases one’s self-confidence is low when he feels rejected by society. For example, a person who loses his job gives a wide berth to other people for fear of being questioned about his work. However, this isn’t right at all. One needs to think along positive lines in spite of failures. After all it is your life and you have every right to live your life as you wish.The challenge lies in not allowing your self-confidence to decrease. It is very important to believe in yourself. Self belief is the secret to success. When success doesn’t come to you, you should not allow your self-belief to be affected. Always keep in mind that success is sure to come in time. So, there is nothing wrong with your ability. Whenever lack of success causes you to doubt your ability, don’t forget to remind yourself that quick success does not last long. Also remember not to compare yourself to others. These tips will do a world of good to your confidence.In order to be self-confident, you need to have a lifestyle that is right for you. Create one and live a life as you want to. Leave others to themselves.32. According to the text, what causes people to fear the unknown?A. The low abilities.B. The lack of security.C. The loss of self-confidence.D. The severe competition in life.33. What does the underlined phrase “gives a wide berth to” in Paragraph 2 mean?A. Introduces something to.B. Holds a birthday party for.C. Makes friends with.D. Keeps away from.34. What is the function of the first paragraph ?A. To explain the meaning of self-confidence.B. To explain why self-confidence is important.C. To show the main topic – to be self-confident.D. To show the reasons that affect one’s self-confidence.35. In the author’s opinion, it’s important that one _____.A. should not forget his failuresB. should follow others’ adviceC. should not lose heartD. should believe life第二节(共5小题;每小题2分，满分10分)根据短文内容，从短文后的选项中选出能填入空白处的最佳选项，并在答题卡上将该项涂黑。

西安高三英语试题及答案一、听力理解（共20分）1. What did the man do last weekend?A. He went to a concert.B. He visited his grandparents.C. He stayed at home.2. How much will the woman pay for the dress?A. $50.B. $60.C. $70.3. What are the speakers mainly talking about?A. A new restaurant.B. A cooking recipe.C. A food review.4. Why is the man worried?A. He missed the bus.B. He lost his wallet.C. He forgot his appointment.5. What is the woman's opinion about the movie?A. It's too long.B. It's very exciting.C. It's quite boring.二、阅读理解（共30分）Passage 16. What is the main idea of the passage?A. The importance of sleep.B. The effects of sleep deprivation.C. The benefits of taking naps.7. According to the passage, which of the following is a sign of sleep deprivation?A. Irritability.B. Increased appetite.C. Enhanced memory.8. What does the author suggest to improve sleep quality?A. Drinking coffee before bed.B. Exercising regularly.C. Avoiding electronic devices before sleep.Passage 29. What is the purpose of the article?A. To introduce a new technology.B. To explain a scientific discovery.C. To discuss the impact of climate change.10. Which of the following is NOT mentioned as a solution to the problem?A. Reducing carbon emissions.B. Planting more trees.C. Building more dams.11. What can be inferred from the passage?A. The situation is improving.B. Immediate action is required.C. The problem is temporary.Passage 312. Who is the intended audience of the text?A. Students.B. Teachers.C. Parents.13. What is the main topic of the text?A. Study habits.B. Time management.C. Stress reduction.14. According to the text, which of the following is NOT a recommended strategy?A. Setting realistic goals.B. Procrastinating on assignments.C. Taking regular breaks.15. What is the author's tone throughout the article?A. Encouraging.B. Critical.C. Neutral.三、完形填空（共20分）16. A. althoughB. becauseC. if17. A. decidedB. forgotC. remembered18. A. excitedB. nervousC. relaxed19. A. preparedB. surprisedC. disappointed20. A. finallyB. unfortunatelyC. surprisingly四、语法填空（共15分）21. The museum, ________ (locate) in the city center, is open to the public for free.22. ________ (not leave) any trash behind when you go out.23. She is one of the most ________ (polite) students I have ever met.24. ________ (careful) you are, ________ (little) mistakesyou will make.25. The book is ________ (interest) to me than that one.五、短文改错（共15分）26. First, make sure that you understand the question clearly.27. One of the most important thing to remember is to stay calm.28. It's better to do the easy question first and leave the difficult one for last.29. If you are not sure about an answer, make an educated guess.30. Finally, double check your work to make sure that there are no mistakes.答案一、听力理解1. B2. C3. A4. B5. C二、阅读理解6. A7. A8. C9. C10. C11. B12. A13. A14. B15. C三、完形填空16. B17. A18. A19. B20. A四、语法填空21. located22. Don't leave23. polite24. The more careful, the fewer25. more interesting五、短文改错26. correctly27. things28. questions, last29. to the30. there aren't。

安徽大学本科毕业论文（设计、创作）题目：变量代换在积分计算中的应用学生姓名：陈雷学号：A00814148院（系）：数学科学学院专业：数学与应用数学入学时间：2008年9月导师姓名：施敏加职称/学位：博士导师所在单位：安徽大学数学科学学院完成时间：2012 年 5 月变量代换在积分计算中的应用摘要积分运算是高等数学中重要的内容，而变量代换在积分计算中应用非常的广泛。

对于不定积分，变量代换的应用可以化简一些常规解法无法解决的复杂积分。

对于多重积分、曲线积分、曲面积分，一定程度上可以说，解决这些积分计算问题的关键就是找到合适的变换，化简积分区域和积分函数。

对于一些复杂的积分只要选取适当的变量代换，问题将迎刃而解；同时，对于同一个问题，采取不同的变量代换，解题的简便程度也将大不相同。

关键词：变量代换；积分计算；不定积分；多重积分；曲线积分；曲面积分Variable substitution used in integral calculationAbstractIntegral calculation is a very important part in Highter Mathematics , Variable substitution is widely used in integral calculation . For Indefinite integral ,the application of variable substitution can simplify some complex intergral which can’t be solved with the conventional solutian. For multiple integrals , curve integral and surface integrals, to a certain extent , the key to solve this problems is to find the appropriate variable substitution which can simplify the integral region and the Integral function. Some complex integral will be easy solved with suitable method of Variable substitution. And, Addressed one problem of integral calculation with different Variable substitutions will get different simple levels .Keywords: integral calculation ;indefinite integral；integral calculation；multiple integrals；curve integral；surface integrals目录第一章绪论 (1)1.1 变量代换应用简介 (1)1.2 本文的主要内容及组织结构 (1)第二章变量代换在不定积分、定积分、反常积分计算中的应用 (2)2.1 先讨论变量代换在不定积分计算中的应用 (2)2.1.1不定积分变量代换简介 (2)2.1.2 常见的计算不定积分的变量代换 (3)2.2变量代换在定积分、反常积分计算中的应用 (8)第三章变量代换在二重积分计算中的应用 (9)3.1 二重积分的变量代换原则 (9)3.2 二重积分的一般变量代换 (9)3.3 二重积分的极坐标变换 (12)3.3.1 二重积分的极坐标变换简介 (12)3.3.2 二重积分的极坐标变换举例 (13)第四章变量代换在n重积分计算中的应用 (17)4.1 n重积分变量代换简介 (17)4.2 n重积分的特殊变量代换 (17)4.2.1 三重积分的柱面坐标变换与球面坐标变换 (17)4.2.2 n重积分的球面坐标变换 (20)4.3 n重积分的一般变量代换 (21)第五章变量代换在曲线、曲面积分计算中的应用 (23)5.1 变量代换在第一类曲线积分中的应用 (23)5.1.1 第一类曲线积分简介 (23)5.1.2 第一类曲线积分的计算公式 (23)5.1.3 变量代换技巧在第一类曲线积分中的应用 (23)5.1.4 举例分析 (23)5.2 变量代换在第一类曲面积分中的应用 (24)5.2.1 第一类曲面积分简介 (24)5.2.2 第一类曲面积分的计算公式 (24)5.2.3 变量代换技巧在第一类曲面积分中的应用 (25)5.2.4 举例分析 (25)5.3 变量代换在第二类曲线积分中的应用 (26)5.3.1 第二类曲线积分简介 (26)5.3.2 第二类曲线积分计算公式 (26)5.3.3 变量代换技巧在第二类曲线积分中的应用 (27)5.4 变量代换在第二类曲面积分中的应用 (27)5.4.1.第二类曲面积分简介 (27)5.4.2 变量代换技巧在第二类曲面积分中的应用 (27)第六章结束语 (28)参考文献 (29)致谢 (30)第一章绪论1.1 变量代换应用简介变量代换在积分的计算中有很重要的作用，尤其在计算多重积分、曲线积分、曲面积分中应用最广泛。