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Choose the correct answer. Area lying between the curves y^2 = 4x and y = 2x is:

Choose the correct answer.

Q : 7         Area lying between the curves \small y^2=4x and \small y=2x is

                (A)   \small \frac{2}{3}            (B)  \small \frac{1}{3}            (C)  \small \frac{1}{4}            (D)  \small \frac{3}{4}

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The area lying between the curve,  \small y^2=4x and \small 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).

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

Therefore the Area OBAO =  Area(\triangle OCA) -Area (OCABO)

=2\left [ \frac{x^2}{2} \right ]_0^1 - 2\left [ \frac{x^{\frac{3}{2}}}{\frac{3}{2}} \right ]_0^1

=\left | 1-\frac{4}{3} \right | = \left | -\frac{1}{3} \right | = \frac{1}{3} units.

Thus the correct answer is B.

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