The area (in sq. units) bounded by the curve $y = \cos x$ and x-axis between $x = 0$ and $x =\frac{3\pi}{2}$ is

3

The correct answer is Option (3) → 3

$\text{Area}=\int_{0}^{\frac{3\pi}{2}}|\cos x|\,dx=\int_{0}^{\frac{\pi}{2}}\cos x\,dx+\int_{\frac{\pi}{2}}^{\frac{3\pi}{2}}-\cos x\,dx$

$\int_{0}^{\frac{\pi}{2}}\cos x\,dx=\sin x\big|_{0}^{\frac{\pi}{2}}=1$

$\int_{\frac{\pi}{2}}^{\frac{3\pi}{2}}-\cos x\,dx=-\sin x\big|_{\frac{\pi}{2}}^{\frac{3\pi}{2}}= -\big(\sin\frac{3\pi}{2}-\sin\frac{\pi}{2}\big)=2$

$\text{Area}=1+2=3$