Question

Area of loop of the curve $r = a \sin \, 2 \theta$ is

• A. $\frac{\pi a^2}{8}$
• B. $\frac{\pi a}{8}$
• C. $\frac{ 3 \pi a^2}{8}$
• D. $\frac{ 7\pi a^2}{8}$

Answer 1

Answer: (C)

$\frac{ 3 \pi a^2}{8}$

Answer 2

Given equation is equation of a curve in polar form is $r = a \sin 2 \theta$ $r = 0 \Rightarrow \theta = \frac{\pi}{2}$ similarly, $\theta = 0 , \frac{\pi}{2}, \pi, , \frac{3\pi}{2} , 2 \pi$ Required area = Area of one loof $= \int{\pi/2}_0 \frac{1}{2} r^2 d \theta$