Question

Area bounded by the curve 2y2 = 3x and the line x+y = 3 outside the circle (x-3)2 + y2 = 2 and above the x-axis is A. The value of 4(π +4A) is?

Answer 1

The correct answer is : 42

A = required area
$=\int\limits^{\frac{3}{2}}_0\left[(3-y)-(\frac{2y^2}{3})\right]dy-\pi(\sqrt2)^2.\frac{1}{8}$
$⇒\left(3y-\frac{y^2}{2}-\frac{2}{9}y^3\right)\big|^{\frac{3}{2}}_{0}-\frac{\pi}{4}$
$⇒3.\frac{3}{2}-\frac{9}{8}-\frac{2}{9}.\frac{27}{8}-\frac{\pi}{4}$
$⇒\frac{36-9-6}{8}-\frac{\pi}{4}$
$=\frac{21}{8}-\frac{\pi}{4}$
$⇒4(\pi+4A)=4(\frac{21}{2})$
$=42$