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Question

Mathematics Question on Parabola

The area of the region enclosed between the parabolas y 2 = 2 x – 1 and y 2 = 4 x – 3 is

A

⅓

B

⅙

C

⅔

D

¾

Answer

⅓

Explanation

Solution

The correct option is(A): 13\frac{1}{3}

Area of the shaded region

The area of the region enclosed between the parabolas

=2∫01(y2+34−y2+12)dy=2∫_0^1(\frac{y^2+3}{4}-\frac{y^2+1}{2})dy

=2∫01(14−y24)dy=2∫_0^1(\frac{1}{4}-\frac{y^2}{4})dy

=2[14−112]=13=2[\frac{1}{4}-\frac{1}{12}]=\frac{1}{3}