Question

The area of the region bounded by the curves $y=\sin \pi x$ and $x$-axis is ____, where $x\in [0,2]$

• A. $\pi$
• B. $\frac{4}{\pi }$
• C. $2\pi$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is B $\frac{4}{\pi }$

from the diagram we can see that the area above and beow are same for x belongs to $[0,2]$

therefore the area =$2{\int }_0^1\sin \left(\pi x\right)=\frac{-\cos \left(\pi x\right)}{\pi }$

substituting the limits we get $2$($\frac{2}{\pi }$)=$\frac{4}{\pi }$