question_answer

The area bounded by the parabola\[{{y}^{2}}=8x\] and its latusrectum, is

A)  \[\frac{16}{3}\]sq units

B)  \[\frac{32}{3}\]sq units

C)  \[\frac{8}{3}\]sq units

D)  \[\frac{64}{3}\]sq units

Correct Answer: B

Solution :

The given equation of parabola is \[{{y}^{2}}=8x\]                ...(i) \[\therefore \]Required area \[=2\int_{0}^{2}{\sqrt{8x}}dx=2.2\sqrt{2}\int_{0}^{2}{\sqrt{x}}dx\] \[=4\sqrt{2}\left[ \frac{{{x}^{3/2}}}{3/2} \right]_{0}^{2}=4\sqrt{2}\left[ \frac{2\sqrt{2}}{3/2} \right]\] \[=\frac{32}{3}\]sq units