Find the volume of the solid formed when the region bounded by the curves y=x3, y=1, and x=0 is rotated about the y-axis, use washer AND shell methods
Disc/Washer:
Ωx2dy = Ω(y1/3)2dy = Ωy2/3dy
Volume:
V = 0∫1 Ωy2/3dy = Ω{(3y5/3)/5} = 3Ω/5
Shell:
2Ωy(x)dx = 2Ωx(x3)dx = 2Ωx4dx
Volume:
V = 0∫1...