question_answer

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

A)  16/3 sq unit      

B)  32/3 sq unit

C)  8/3 sq unit         

D)         64/3 sq unit

E)  4/3 sq unit

Correct Answer: B

Solution :

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