Question

How to solve this integral...

Answer 1

\[\int\limits_{0}^{a}r ^{3}/\sqrt{a ^{2}-r ^{2}}*dr\]

Answer 2

http://www.wolframalpha.com/input/?i=x^3%2Fsqrt%28a^3+-+x^2%29

Answer 3

this will help you

Answer 4

\[\int \frac{r^3}{\sqrt{a^2-r^2}}dr\]

let u=r^2
du=2r dr
dr=du/2r

\[=\int \frac{ur}{\sqrt{a^2-u}}\frac{du}{2r}\]\[\int \frac{u}{2\sqrt{a^2-u}}du\]

Answer 5

let s=a^2-u so u=a^2-s
ds=-du
du=-ds

\[\frac{-1}{2}\int \frac{a^2-s}{\sqrt{s}}ds\]\[=\frac{-1}{2}\int \frac{a^2}{\sqrt{s}}-s/s^{0.5}ds\]\[=\frac{-1}{2}\int \frac{a^2}{\sqrt{s}}-\sqrt{s} ds\]

Answer 6

And then solve normally :)

Answer 7

Thanks