Question

Area bounded by the curve $y=cosx$ 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, $y=cosx\dots \left(i\right)$
between $x=0$ to $x=\frac{3\pi }{2}$
Required area = area of shaded region
$=\underset{0}{\overset{\pi /2}{\int }}cosxdx+\left|\underset{\pi /2}{\overset{3\pi /2}{\int }}cosxdx\right|$


$={\left[sinx\right]}_0^{\pi /2}+\left|{\left[sinx\right]}_{\pi /2}^{3\pi /2}\right|$

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