Question

Area bounded by the curve $y = cos \,x$ between $x = 0$ and $x=\frac{3\pi}{2}$ is

• A. $1$ sq. unit
• B. $2$ sq. units
• C. $3$ sq. units
• D. $4$ sq. units

Answer 1

Answer: (C)

We have, $y = cos\,x \quad\ldots\left(i\right)$
between $x=0$ to $x=\frac{3\pi}{2}$
Required area = area of shaded region
$=\int\limits_{0}^{\pi /2}cos\,x\,dx+\left|\int\limits_{\pi /2}^{3\pi/ 2} cos\,x\,dx\right|$


$=\left[sin\,x\right]_{0}^{\pi/ 2}+\left|\left[sin\,x\right]_{\pi /2}^{3\pi /2}\right|$

$=1+\left|\left(-1-1\right)\right|$
$= 1 + 2 = 3$ sq. units