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Q.
The area bounded by the curve $y = sec^{2} x$, $y = 0$ and $|x|=\frac{\pi}{3}$ is
Application of Integrals
Solution:
We have, $y=sec^{2}x$ and $y=0$ and $x=\frac{\pi}{3}$, $-\frac{\pi}{3}$
Required area = area of shaded region
$=\int\limits_{-\pi /3}^{\pi /3} sec^{2}\,x\,dx=\left[tan\,x\right]_{-\pi/ 3}^{\pi /3}=2\sqrt{3}$ sq. units
