问题 问答题

求由曲线y=x,y=lnx及y=0,y=1围成的平面图形的面积S,并求此平面图形绕丁轴旋转一周所得旋转体的体积Vx.

答案

参考答案:本题考查的知识点是曲边梯形面积的求法及旋转体体积的求法.

解析:首先应根据题目中所给的曲线方程画出封闭的平面图形,然后根据此图形的特点选择对x积分还是对y积分.选择的原则是:使得积分计算尽可能的简单或容易算出.本题如果选择对x积分,则有
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这显然要比对y积分麻烦.
在求旋转体的体积时一定要注意是绕x轴还是绕y轴旋转.历年的试题均是绕。轴旋转,而本题是求绕丁轴旋转的旋转体的体积.
旋转体的体积计算中最容易出现的错误(在历年的试卷均是如此)是:
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考生一定要牢记:Vx=V2-V1,即分别计算两个旋转体所成的旋转体体积之差.本题为
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解 画出平面图形,如图7-3所示的阴影部分,则有阴影部分的面积
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阅读理解

The dog that gave us the most trouble was a beagle (猎兔犬) named Murphy.As far as I’m concerned, the first thing he did wrong was to turn into a beagle.I had seen him bounding around on the other side of a pet-shop window, and I went in and asked the man, “How much is that adorable fox terrier (小猎狗) in the window?” Did he say “That adorable fox terrier is a beagle”? No, he said, “Ten dollars, lady.” Now, I don’t mean to say one word against beagles.They have rights just like other people.But it is a bit of a shock when you bring home a small ball of fluff (绒毛) in a shoebox, and three weeks later it’s as long as the sofa.

Murphy was the first dog I ever trained personally, and I was delighted at the enthusiasm with which he took to the newspaper.It was some time later that we discovered, to our horror, that—like so many dogs—he had grasped the letter but not the spirit of the thing.Until the very end of his days he felt a real sense of duty whenever he saw a newspaper—any newspaper—and it didn’t matter where it was.I can’t bring myself to go into the details, except to mention that we were finally forced to keep all the papers in the bottom of the icebox.

He had another habit that used to leave us open to a certain amount of criticism from our friends.He never climbed up on beds or chairs or sofas.But he always sat on top of the piano.In the beginning we used to try to pull him off.But after a few noisy fights in which he knocked a picture off the wall, scratched the piano, and smashed a lamp, we just gave in—only to discover that he hopped up and down as skillfully as a ballet dancer.

Nowadays if I go anywhere, I just ask if they have a dog.If they do, I say, “Maybe I’d better keep away from it—I have bad allergy.” This sometimes annoys the host.But it works.It really works.

56.The writer uses a hyperbole (夸张) in Paragraph 1 to suggest that the dog grew  _____________.

A.surprisingly lovable B.comfortable in the house

C.too fierce to tolerate D.larger than expected

57.Which sentence shows the author’s inability to train Murphy?

A.I had seen him bounding around on the other side of a pet-shop window.

B.We were finally forced to keep all the papers in the bottom of the icebox.

C.He never climbed up on beds or chairs.

D.Nowadays if I go anywhere, I just ask if they have a dog.

58.What can you infer from the second paragraph?

A.The writer tried to train Murphy to fetch newspapers but in vain.

B.Like other dogs, Murphy hated newspapers.

C.Murphy learned to help the writer clean the papers.

D.Murphy liked fetching letters rather than newspapers.

59.Which can be the best title of the passage?

A.Murphy—My Favorite Dog    B.Murphy—An Adorable Dog

C.Murphy Gave Me Trouble      D.Murphy Turned Into A Beagle

单项选择题