Question

Find the area of the region bounded by $C:y=tanx$, tangent drawn to C at $x=\pi /4$ and the x-axis.

Answer 1

$Area={\int }_0^{\pi /4}\tan x=[log\sec x{]}_0^{\pi /4}=logsec(\pi /4)-log1=log(\sqrt{2})-0=log(\sqrt{2})=\frac{1}{2}log2$