Question

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

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

Answer 1

The Correct Option is B

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[\(\frac{x^2}{2}\)]10-2[x³/2/3/2]10

=|1-\(\frac{4}{3}\)|

=|-\(\frac{1}{3}\)|

=\(\frac{1}{3}\)units

Thus, the correct answer is B.