题目内容

设有半径为R(米)、长为L(米)的均匀网柱体，平放在深度为2R(米)的水池中(圆柱体的侧面与水面相切)，设圆柱的密度是水密度的μ倍(μ＞1)，现将网柱体平移出水面，需做多少功

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设D是曲线y=2x-x2与x轴同成的平面图形，直线y=kx把D分成D1与D2上下两部分，若D1的面积S1与D2的面积S2之比S1:S2=1:7．求平面图形D1绕y轴旋转一周所得旋转体的体积．

Section ADirections: This section is to test your ability to give proper answers to questions. There are 5 recorded questions in it. After each question, there is a pause. The questions will be spoken two times. When you hear a question, you should decide on the correct answer from the 4 choices marked A), B), C) and D) given in your test paper. Then you should mark the corresponding letter on the Answer Sheet with a single line through the center.

A. Your bike is old.
B. In the shop.
C. At the street corner.
D. Mother bought it for me.

一个面密度为ρ(x)=x2，曲线y=4-x2和x轴围成的平而物体，用定积分求： (Ⅰ)质量； (Ⅱ)关于x轴，y轴的静力矩； (Ⅲ)质心．

设函数f(x)在(0，+∞)连续，且对任意x＞0，y＞0，积分与x无关，仅依赖于y，f(2)=2，求(x＞0)．