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Question

Mathematics Question on applications of integrals

Area lying between the curve y2=4x and y=2x is

A

23\frac{2}{3}

B

13\frac{1}{3}

C

14\frac{1}{4}

D

34\frac{3}{4}

Answer

13\frac{1}{3}

Explanation

Solution

The area lying between the curve,y2=4x and y=2x,is represented by the shaded

area OBAO as

The points of intersection of these curves are O(0,0)and A(1,2).

We draw AC perpendicular to x-axis such that the coordinates of C are(1,0).

∴Area OBAO=Area(ΔOCA)-Area(OCABO)

=

\int_{0}^{4} 2x \,dx - $$$$\int_{0}^{4} 2\sqrt{x} \,dx

=2[x22\frac{x^2}{2}]10-2[x3/2/3/2]10

=|1-43\frac{4}{3}|

=|-13\frac{1}{3}|

=13\frac{1}{3}units

Thus, the correct answer is B.