Question

Find the volume of the solid that results when the area of the region enclosed by y=x^3, x=-1, and x=1 is rotated about the x-axis

Answer 1

$V=\int_a^b\pi y^2dx=\int_{-1}^1\pi x^6dx=\frac{\pi}{7}x^7|_{x=-1}^{x=1}=\frac{2\pi}{7}.$