1. ## Help with Integration

I am not getting integrals that are improper! Here are 2 questions that I'm not sure about: The integral from 0 to infinity of (x) / (x^2+33)2 dx. Also, the integral from negative infinity to infinity of (30-x^4) dx. I think the last integral is convergent since its an upside down parabola.

2. $\displaystyle \int_{0}^{L}\frac{x}{(x^{2}+33)^{2}}dx$

Let $\displaystyle u=x^{2}+33, \;\ \frac{du}{2}=xdx$

You get:

$\displaystyle =\frac{1}{66}-\frac{1}{2(L^{2}+33)}$

$\displaystyle \lim_{L\to {\infty}}\left[\frac{1}{66}-\frac{1}{2(L^{2}+33)}\right]$

$\displaystyle =\frac{1}{66}$

It converges.

3. Okay, I just don't get how you got 1/66, I know that 2 times (1/33) is 1/66 but what about the x^2+33 squared?

4. Originally Posted by Holly3
Okay, I just don't get how you got 1/66, I know that 2 times (1/33) is 1/66 but what about the x^2+33 squared?
You don't know that $\displaystyle \lim _{L \to \infty } \frac{1}{{2\left( {L^2 + 33} \right)}} = 0$??

5. No, I was confused before why (1) over (x^2+33)^2 got 1/66, but I understand now! And I think for my second question, I think the answer is negative infinity, but wouldn't that be divergent? The second question was the integral from neg. infin. to pos infin. of (30-x^2). I'm not sure if I did something wrong, but it seems like the answer is negative infinity. Does that make sense?