In this question, we have to find the volume of the region bounded by the given curves and we use polar coordinates to find the required volume . Answer and Explanation: Let {eq}x=r cos \theta , y =r sin \theta,dA=dxdy=rdrd \theta {/eq...
Answer to: Find the volume using cylindrical shells of the region bounded by the curves y = x and y = x^2 rotated about the line y = 1. By...
定积分求体积Sketch the region Ω bounded by the curves and use the shell method to find the volume of the solid generated by revolving Ω about the y-axis.x=|y|,x=2-y^2
Find the volume of the solid obtained by rotating the region bounded by the curves y = x^4 and y = 1 about y = 4. Find the volume of the solid obtained by rotating the region bounded by the curves: y = x^2/9, x...
The volume when the region rotated around thex-axis is determined as: V=π∫ab[(f(x))2−(g(x))2]dx Answer and Explanation:1 The given curves are : y1(x)=5x−x2andy2(x)=x Now, we determine the x-coordinates ...
结果1 题目 Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given curves about the line y=25.y=25-x^2, y=25, x=5; 相关知识点: 试题来源: 解析 625π 反馈 收藏 ...
Question: [Volumes](a) Find the volume of the solid obtained by rotating the region bounded by thefollowing curves around the x-axis.y=x3,y=0,x=0,x=1(b) Calculate the volume of the solid obtained by rotating the region bounded b...
求绕y轴旋转后的体积.A ball of radius 15 has a round hole of radius 3 drilled through its center.Find the volume of the resulting solid.Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.y=0,y=(cos6x),x=0,x=pi/12, ...
First, graph the region bounded by these curves. Set up a cylindrical shell that is parallel to the axis of rotation. What happens in the shell method is that we revolve the infinitesimal cylindrical shells about the y-axis and have a solid that looks like the one on the right....
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line, using disk/washer method. a)Sketch the region b)sketch the solid c)sketch and label a typical disk or washer ...