The area between the curve y 2 = 4 a x , the x -axis and the lines x = 0 and x = a is:

Question

The area between the curve $y^{2} = 4 a x$ , the $x$ -axis and the lines $x = 0$ and $x = a$ is:

Smart Achievers · Accepted Answer

(2)

Ans. $\frac{8}{3} a^{2}$ sq. units

Explanation:

$Required area = 2 \int_{0}^{a} y d x$

$= 2 \int_{0}^{a} \sqrt{4 a x} d x$

$= 4 \sqrt{a} \int_{0}^{a} x^{1 / 2} d x$

$= 4 \sqrt{a} \times \frac{2}{3} {[x^{3 / 2}]}_{0}^{a}$

$= \frac{8 \sqrt{a}}{3} \cdot a \sqrt{a}$

$= \frac{8}{3} a^{2} sq. units.$

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