Question

微积分题目

The portion of the graph
y = tan^(−1) x
between x = 0 and x = 1 is rotated around the y axis to form a container. The container is filled with water. Use n = 6 subintervals and Simpson's rule to approximate the work required to pump all of the water out over the side of the container. Give your answer in decimal form.
(Distance is measured in meters, the density of water is 1000 kg/m3, and use 9.8 m/s2 for g.)

Answer 1

我就随便做做，别认真了哟，因为实在找不到那个横截面的面积公式

所以就用不了定积分的方法了，更别说用Simpson法则。。

或许我想到后会有后补，到时候再算吧

Answer 2

题目翻译：将y= tan^(−1) x在x从0到1的一部分图像绕y轴旋转，形成一个装满水的容器。要求从容器中抽出所有的水，并利用六等分的子区间和辛普森公式去近似求解工作量。答案用小数形式表示。（距离的单位是m，水的密度是1000 kg/m3，g=9.8 m/s^2 ）
你先看看题目是不是这个意思？