How can I show that $\int_{0}^1\int_{0}^1 \frac{1}{1-xy}dxdy=\frac{\pi^2}{6}$ through substitution?

Asked Mar 12 '18 at 14:35

Active Mar 12 '18 at 14:53

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I know that the answer can be arrived through integration of geometric series to evaluate $\zeta(2)$, but i was wondering if the result could be attained through a sub?

asked Mar 12 '18 at 14:35

aleden

4,007

Sure, just let $u=x$, $du=dx$ then do that – Mar 12 '18 at 14:39
2

Try $u=\dfrac{x+y}{2}$ and $v=\dfrac{y-x}{2}$. – projectilemotion Mar 12 '18 at 14:40

How can I show that $\int_{0}^1\int_{0}^1 \frac{1}{1-xy}dxdy=\frac{\pi^2}{6}$ through substitution?

0 Answers0