Question

If the area bounded by $y=x,y=sinx$ and $x=\frac{\pi }{2}$ is $\left(\frac{\left(\pi \right)^{2}}{k} - 1\right)$ sq. units, then the value of $k$ is equal to

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (D)

Required area $=ar\left(\Delta A O B\right)-\displaystyle \int _{0}^{\frac{\pi }{2}}sin xdx$
$=\underset{\frac{1}{2} \cdot b a s e \cdot h e i g h t}{\underbrace{\frac{1}{2} \cdot \frac{\pi }{2} \cdot \frac{\pi }{2}}}-1$
$=\frac{\pi ^{2}}{8}-1$ sq. units