Question

Find the area of the closed figure bounded by the following curves $y=$ $\frac{1}{{\cos }^{2}x}$, $y=0,x=0,x=$ $\frac{\pi }{4}$

Answer 1

$y=\frac{1}{{\cos }^{2}x}$ (given)

$y={\sec }^{2}x$

$A={\int }_0^{\pi /4}{\sec }^{2}xdx$

Area $=[\tan x{]}_0^{\pi /4}$

Area $=\tan \frac{\pi }{4}-\tan 0$

Area $=[1-0]$

Area = $1$