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Question: Find the area bounded by the parabola \(y ^ { 2 } = 4 x\)and its latus rectum...

Find the area bounded by the parabola y2=4xy ^ { 2 } = 4 xand its latus rectum

A

83\frac { 8 } { 3 }

B

43\frac { 4 } { 3 }

C

163\frac { 16 } { 3 }

D

None of these

Answer

83\frac { 8 } { 3 }

Explanation

Solution

Since the curve is symmetrical about x-axis, therefore the required area

=2∫01ydx= 2 \int _ { 0 } ^ { 1 } y d x =2∫014xdx= 2 \int _ { 0 } ^ { 1 } \sqrt { 4 x } d x

=4⋅23[x32]01=83= 4 \cdot \frac { 2 } { 3 } \left[ x ^ { \frac { 3 } { 2 } } \right] _ { 0 } ^ { 1 } = \frac { 8 } { 3 }