Question

Area bounded between the curve $ x^2 = y $ and the line $ y = 4x $ is

• A. $ \frac{32}{3} $ sq units
• B. $ \frac{1}{3} $ sq units
• C. $ \frac{8}{3} $ sq units
• D. $ \frac{16}{3} $ sq units

Answer 1

Answer: (A)

Given curves are $x^{2}=y$ and $y=4 x$
Intersection points are $(0,0)$ and $(4,16)$
$\therefore $ Required area $=\int \limits_{0}^{4}\left(4 x-x^{2}\right) d x$
$=\left[\frac{4 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{4} $
$=\left[32-\frac{64}{3}\right] $
$=\frac{32}{3} $ sq unit