Question

Use the method of a cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y - axis.

Answer 1

\[y=x^3, y=0, x=1, x=2\]

Answer 2

\[V=\int\limits_{x=1}^{x=2}ydS=\int\limits_{x=1}^{x=2}x^3(2\pi x)dx=2 \pi \int\limits_{x=1}^{x=2}x^4dx\]

Answer 3

Correct!

Answer 4

Thank you :)

Answer 5

you are welcome