Question

The area in the first quadrant enclosed by the X-axis under the curve $x^2+y^2=4$ and the line $x=\frac{y}{\sqrt{3}}$ is:

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

Answer 1

The correct option is B $\frac{2\pi }{3}$ sq. units

$y=\sqrt{4-x^2}$
$\stackrel{1}{\underset{0}{\int }}\sqrt{3}xdx+\stackrel{2}{\underset{1}{\int }}\sqrt{4-x^2}dx$
$=\sqrt{3/2}+2/3[0-\sqrt{3}]$