Question

The area of the region bounded by the curves $f\left(x\right)=\sin \pi x$ and x-axis for $x\in [-1,2]$ is

• A. $8\pi$
• B. $\frac{8}{\pi }$
• C. $\frac{6}{\pi }$
• D. $6\pi$

Answer 1

The correct option is C $\frac{6}{\pi }$

$\sin \pi x$ is periodic in nature.
Hence, $A=3\underset{0}{\overset{1}{\int }}\sin \pi xdx$
$=3{\left[\frac{-\cos \pi x}{\pi }\right]}_0^1$
$=3[\frac{1}{\pi }+\frac{1}{\pi }]$
$=\frac{6}{\pi }$