Question

the region enclosed by the graph y=x^2, the line x=2,and the x-axis is rearopund the y-axis. what the volume of the solid generated?

Answer 1

Here is my solution:

\[\int\limits_{0}^{2}(2\pi)(x)(x^2)\]

then, then that is \[(2\pi)\int\limits_{0}^{2}(x^4)/4\]

then you receive 2pi*(4-0) and get \[8\pi\]

someone should check this as this is just what I got.
Hope it helps

Answer 2

\[V=\pi\left(\int\limits_0^4 2^2dy-\int\limits_0^4(\sqrt{y})^2dy\right)=\pi\left(4\int\limits_0^4 dy-\int\limits_0^4 ydy\right)=\]\[=\pi\left(16-8\right)=8\pi\]