平移得到新的
y=ƒ(x)=sinx-1
体积
V[欲求]=V[1]-V[2]
V[1]为[0,π]长,半径为1的圆柱体体积.
V[2]为ƒ(x)=sinx-1与y=0所围在[0,π]绕y=0旋转得到体积.
V[1]=π
V[2]=∫πf(x)^2dx[from 0 to π]
=∫π(sinx-1)^2dx[from 0 to π]
=∫π(sin(x)^2-2sinx+1)dx[from 0 to π]
=∫π((1-cos2x)/2-2sinx+1)dx[from 0 to π]
=∫π(-cos2x)/2)dx[from 0 to π]
+∫π(-2sinx)dx[from 0 to π]
+∫π(3/2)dx[from 0 to π]
=0+2πcosx[from 0 to π]+3π^2/2
=3π^2/2-4π
V[欲求]
=V[1]-V[2]
=π+(3π^2/2-4π)
=5π-3π^2/2