The area of region bounded by curve $y^2=4x$ and the lines $y=2$ and $x=0$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{2}{3}$
$y^2=4x$, $y=2$, $x=0$
at $y=2$
$y^2=4x$
$2^2=4x$
$⇒x=1$
so required area = $2×1-\int\limits_0^12\sqrt{x}dx$
$=2-2\left[\frac{2}{3}x^{3/2}\right]_0^1$
$⇒2-\frac{4}{3}⇒\frac{2}{3}$ sq. units