# Math Help - mixed variable double integral..

1. ## mixed variable double integral..

$\int_{0}^{2}\int_{\frac{1}{2}x^{2}}^{x}\frac{x}{x^ {2}+y^{2}}dydx$

how to approach
it?

2. You should reverse the order of integration...

3. What is your problem exactly?

$\int \dfrac{x}{x^2+y^2} \, dy=arctan\left(\dfrac{y}{x}\right)$

4. but i have variables in the intervals
?

5. Originally Posted by General

$\int \dfrac{x}{x^2+y^2} \, dy=arctan\left(\dfrac{y}{x}\right)$
i cant solve it like this
i ned to get rid of one integral then the other

6. Why?

$\displaystyle \int_{\frac{1}{2}x^{2}}^{x}\frac{x}{x^{2}+y^{2}}dy =arctan(1)-arctan\left(\dfrac{1}{2}x\right)$

7. Originally Posted by transgalactic
i cant solve it like this
i ned to get rid of one integral then the other
Yes, you can solve it like that. Just evaluate that integrand at the upper and lower limits, so that you get a function in x only- then do the second integration.