Question

The area of the region bounded by $y={\sin }^{4}x,x$-axis and ordinates $x=0,x=2\pi$ (in sq. units)

• A. $\frac{3\pi }{4}$
• B. $\frac{\pi }{4}$
• C. $\frac{3\pi }{2}$
• D. $3\pi$

Answer 1

The correct option is A $\frac{3\pi }{4}$

$y={\sin }^{4}x=\stackrel{\pi }{\underset{0}{\int }}{\sin }^{4}xdx$
$4\stackrel{\pi /2}{\underset{0}{\int }}{\sin }^{4}x$
$=\left(3\right)\left(\frac{1}{2}\right)\left(\pi /2\right)$
$=3\pi /4sq.units$