Question

The area bounded by $y=\sin \left(\frac{\pi }{2}x\right)$, $x=0,y=0$ and $x=\frac{4}{3}$ is

• A. $\frac{6}{\pi }$
• B. $\frac{3}{\pi }$
• C. $\frac{2}{\pi }$
• D. $\frac{9}{\pi }$

Answer 1

The correct option is B $\frac{3}{\pi }$


The area bounded
$=\underset{0}{\overset{\frac{4}{3}}{\int }}\sin \left(\frac{\pi }{2}x\right)dx=-\frac{2}{\pi }{\left[\cos \left(\frac{\pi }{2}x\right)\right]}_0^{4/3}=-\frac{2}{\pi }[\cos \frac{2\pi }{3}-1]=-\frac{2}{\pi }\times -\frac{3}{2}=\frac{3}{\pi }$