$\displaystyle \int_{0}^{2}\int_{\frac{1}{2}x^{2}}^{x}\frac{x}{x^ {2}+y^{2}}dydx$ how to approach it?
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You should reverse the order of integration...
What is your problem exactly? $\displaystyle \int \dfrac{x}{x^2+y^2} \, dy=arctan\left(\dfrac{y}{x}\right)$
but i have variables in the intervals ?
Originally Posted by General What is your problem exactly? $\displaystyle \int \dfrac{x}{x^2+y^2} \, dy=arctan\left(\dfrac{y}{x}\right)$ i cant solve it like this i ned to get rid of one integral then the other
Why? $\displaystyle \displaystyle \int_{\frac{1}{2}x^{2}}^{x}\frac{x}{x^{2}+y^{2}}dy =arctan(1)-arctan\left(\dfrac{1}{2}x\right)$
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.
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