# Thread: Polar Double Integration help

1. ## Polar Double Integration help

I'm doing polar integration and I'm having some problems.

$\displaystyle 4*\int_{0}^{\frac{\pi}{2}} \int_{0}^{1} ln(r^{2}+1)rdrd\theta$

The answer comes out to

$\displaystyle \pi(ln(4)-1)$ but I always end up with $\displaystyle \pi(ln(2)-1)$

2. Originally Posted by FalconPUNCH!
I'm doing polar integration and I'm having some problems.

$\displaystyle 4*\int_{0}^{\frac{\pi}{2}} \int_{0}^{1} ln(r^{2}+1)rdrd\theta$

The answer comes out to

$\displaystyle \pi(ln(4)-1)$ but I always end up with $\displaystyle \pi(ln(2)-1)$
If you show your working it will be easier to see your mistake.

The only 'hard' bit is finding $\displaystyle \int_{1}^{2} \ln u \, du = 2 \ln (2) - 1$ where $\displaystyle u = r^2 + 1$. Note the integrals terminals (this is probably what you forgot).

3. Originally Posted by mr fantastic
If you show your working it will be easier to see your mistake.

The only 'hard' bit is finding $\displaystyle \int_{1}^{2} \ln u \, du = 2 \ln (2) - 1$ where $\displaystyle u = r^2 + 1$. Note the integrals terminals (this is probably what you forgot).
I would have shown my work but it's two pages long and messy. I think it's because I didn't try substituting. I'll try that thanks.