The area bounded by the parabola y2 = 4ax, its axis and two ordinates x = 4, x = 9 is:

Question

The area bounded by the parabola $y^{2} = 4 a x,$ its axis and two ordinates $x = 4, x = 9$ is:

Smart Achievers · Accepted Answer

(4)

Ans. $\frac{152 \sqrt{a}}{3}$ sq. units

Explanation :

$Shaded area A = 2 \int_{4}^{9} \sqrt{4 a x} d x$

$A = 4 \sqrt{a} \int_{4}^{9} \sqrt{x} d x$

$= 4 \sqrt{a} \times \frac{2}{3} {[x^{3 / 2}]}_{4}^{9}$

$= \frac{8 \sqrt{a}}{3} (9^{3 / 2} - 4^{3 / 2})$

$= \frac{8 \sqrt{a}}{3} (27 - 8)$

$= \frac{152 \sqrt{a}}{3} sq. units.$

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