Question

The area of the region enclosed by
$y≤4x^2, x2≤9y\ and\ y≤4,$
is equal to

• A. $\frac{40}{3}$
• B. $\frac{56}{3}$
• C. $\frac{112}{3}$
• D. $\frac{80}{3}$

Answer 1

Answer: (D)

$\frac{80}{3}$

Answer 2

The correct answer is (D) : $\frac{80}{3}$

Fig..

$y≤4x^2, x^2≤9y, y≤4$
So, required area
$A = 2 \int^{4}_{0} (3\sqrt{y}-\frac{1}{2}\sqrt{y})dy$
$= 2.\frac{5}{2} [\frac{2}{3} y^{\frac{3}{2}}]^{4}_{0}$
$= \frac{10}{3} [4^{\frac{3}{2}}-0]$
$=\frac{80}{3}$