Show that of all rectangles inscribed in a given circle, the squa… - Vidyadip

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Show that of all rectangles inscribed in a given circle, the square has the maximum area.

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$\begin{aligned}
\int_{-a}^a f(x) \cdot d x & =2 \int_0^a f(x) \cdot d x 0, & & \text { if } f(x) \text { is an even function. } \\
& =0, & & \text { if } f(x) \text { is an odd function }
\end{aligned}$
Hence find the value of $\int_{-1}^1 \tan ^{-1} x \cdot d x$