Question

http://puu.sh/28Cox/fb05fec34d (S OPEN LINK TO SEE PROBLEM) I'm learning how to do volume of a solid by plane slicing and one of the problems is to find the volume of a cone by writing dV in terms of u and dy and then integrating. why does the power change from 2 to 3?

Answer 1

in terms of y*

Answer 2

\[\large \pi\int (5-0.5y)^2dy\]
let u=5-0.5y
du = -0.5 dy
-2du = dy
\[\large \pi\int (5-0.5y)^2dy=\pi\int u^2(-2du)=-2\pi\frac{u^3}{3}+C\\\quad=-\frac{2\pi}{3}(5-0.5y)^3+C\]