Question

Integral Calculus (Volumes of Revolution)
Find the volume generated when the area bounded by the curve y=x^4, the y-axis, and y=16. is revolved about the y-axis in the first quadrant.

Answer 1

Graph

Answer 2

What grade is this?

Answer 3

well you can use either slices or cylindrical shells. Slices might be easier for this case.
Best you draw up the question first like so:



So we see each slice/disc area is given by
\[A = \pi r^2 = \pi x^2\]
As the depth of each slice/disc is change in y units
We have

\[V = \lim_{\Delta y \rightarrow 0}\sum_{0}^{16} \pi x^2 \Delta y = \int\limits_{0}^{16}\pi x^2 dy\]
The latter part of this equation you should be familiar with already

Sub in x into this formula (in terms of y and you should evaluate the volume of revolution.