Question

Area of the region enclosed by curve $y=5\sin x;(0\le x\le \frac{\pi }{2})$, X-axis is _______

• A. $5$
• B. $1$
• C. $\frac{5}{2}$
• D. $\frac{1}{5}$

Answer 1

Answer: (A)

$5$

Area of a region bounded by $y=5\sin x$; where $0\le x\le \frac{\pi }{2}$
X axis is $A=\left|I\right|$
where $I={\int }_0^{\pi /2}ydx=5{\int }_0^{\pi /2}\sin xdx=5{[-\cos x]}_0^{\pi /2}=5[0+1]=5$
$\therefore A=\left|I\right|=5unit$