Which of the following integrals correctly computes the volume formed when the region bounded by the curves x^2 + y^2 = 25, x = 4, and y = 0 is rotated around the y-axis?

Question

anonymous · Answer

attachment

anonymous · Answer

@rational

anonymous · Answer

there is no negative before the third answer

solomonzelman · Answer

what I would start from is establishing that your function is $\large\color{black}{ \displaystyle x=\sqrt{25-y^2} }$ https://www.desmos.com/calculator/hf2wmtu6oa

anonymous · Answer

@SolomonZelman okay then?

solomonzelman · Answer

it is kind of hard to do it when I have to adjast my thinking to the choice

anonymous · Answer

does the equ look something like this

anonymous · Answer

$$V=\int\limits dV= \int\limits ((\Pi)R ^{2}-(\Pi)r ^{2})h$$

anonymous · Answer

$$dV= (\Pi) \int\limits ((R ^{2})-(r ^{2}))dx$$

anonymous · Answer

dx should be dy

anonymous · Answer

so does this equation make snese

solomonzelman · Answer

haven't done those in a while, but I would do this:
$\large\color{slate}{\displaystyle\int\limits_{3}^{5}\pi\left(\sqrt{25-y^2}\right)^2~dy}$|dw:1428542811567:dw|