Question: Evaluate the integral
$$\int_0^1\int_x^1 \arctan\left(\frac{y}{x}\right) \ dy\,dx $$
My attempt:
So I've converted the integral into polar coordinates, getting the integral
$$\int_0^\frac{\pi}{4}\int_0^\frac{1}{\cos(\theta)} \theta r\,dr\,d\theta \ =\int_0^\frac{\pi}{4} \frac{\theta }{2\cos^2(\theta)} \, d\theta \ $$
However I have no idea where to go from here? Have I calculated the limits wrong or am I missing something?
Thank you