Question

Need to check disk method volume problem.

Answer 1

A region is bound by the graph of x^2/16 + y^2/4 = 1. Find the volume of the solid formed if it is revolved around the y-axis.

Answer 2

ellipsoid darn it

Answer 3

Yeah, unfortunately.

Answer 4

Really what I need to know is whether I took the volume of the two sides or the entire thing.

Answer 5

Well it looks like you just did the top half, so just multiply by 2 to get the full thing.

When you wrote it, you can determine your bounds by noting the last points are when x=0 and y is at a max, so \[\Large \frac{0^2}{16}+\frac{y^2}{4}=1 \\ \Large y = \pm 2\]
Now you can plug it in, and since it's symmetric, just an even function you see we get that 2* the integral you did, I hope that helps make it a little less ambiguous what you're doing.
\[\Large \int\limits_{-2}^2 f(y)dy = 2 \int\limits_0^2 f(y)dy\]

Answer 6

The top half was just what I needed, I just wanted to make sure I was actually doing it correctly. :p Is the math correct?

Answer 7

Yeah the math is all good.

Answer 8

Awesome, thanks.