# Intergration Problem (Substitution I think)

• Jan 10th 2010, 05:57 AM
jezzyjez
Intergration Problem (Substitution I think)
I have this integral i need to do in the middle of a engineering question and I have looked in a few directions at it and cant seem to crack it!

The integral is
$\displaystyle \int 4r/\sqrt{2-r^2}$

First I took out factor of 4.
Then multiplyed out the square to get

$\displaystyle 4\int(2r-r^3/2-r^2)$

And tried by parts, which didn't go to well.

So im looking at substitution making
$\displaystyle u = 2r -r^3$

so $\displaystyle du = 2-3r^2 dr$

Where do I go from here ....
• Jan 10th 2010, 06:10 AM
CaptainBlack
Quote:

Originally Posted by jezzyjez
I have this integral i need to do in the middle of a engineering question and I have looked in a few directions at it and cant seem to crack it!

The integral is
$\displaystyle \int 4r/\sqrt{2-r^2}$

First I took out factor of 4.
Then multiplyed out the square to get

$\displaystyle 4\int(2r-r^3/2-r^2)$

And tried by parts, which didn't go to well.

So im looking at substitution making
$\displaystyle u = 2r -r^3$

so $\displaystyle du = 2-3r^2 dr$

Where do I go from here ....

What is the derivative of $\displaystyle -4\sqrt{2-r^2}$ ?

CB
• Jan 10th 2010, 06:29 AM
galactus
Trig sub is always an old standby.

$\displaystyle \int\frac{4r}{\sqrt{2-r^{2}}}dr$

Let $\displaystyle r=\sqrt{2}sin(t), \;\ dr=\sqrt{2}cos(t)dt$

Make the subs and it whittles clean down to

$\displaystyle 4\sqrt{2}\int sin(t)dt$

After integrating, to get it back in terms of r, make the resub:

$\displaystyle t=sin^{-1}(\frac{r}{\sqrt{2}})$
• Jan 10th 2010, 01:49 PM
rshekhar.in
Why not substitute
$\displaystyle v=2-r^2$
$\displaystyle dr=-\frac{du}{2r}$
• Jan 10th 2010, 02:13 PM
galactus
Go ahead. I was just offerening an alternative. there are numerous ways to tackle it and most other integrals