double integrals problem

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October 27th 2010, 04:36 PM
Evan.Kimia

double integrals problem

Im doing this problem below:

http://i51.tinypic.com/k96gi8.png

here is the solution and i understand everything except how they integrated the r(sqrt(1+r^2)). could anyone point out how they accomplished that? Thank you.

solution:
http://i56.tinypic.com/2vlqihz.jpg
October 27th 2010, 04:51 PM
harish21

$\displaystyle{\int 2r - r \sqrt{1+r^2} dr = \int 2r dr - \int r \sqrt{1+r^2} dr}$

$\displaystyle{\int 2r dr} = 2 \times \dfrac{r^2}{2} = r^2$

for $\displaystyle{ \int r \sqrt{1+r^2} dr}$ use substitution rule by supposing $u = 1+r^2$

So, $du = 2r \mbox{dr} \implies dr = \dfrac{du}{2}$
October 27th 2010, 05:58 PM
Evan.Kimia

ah, i should of know that.
Thanks a bunch.

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