NDA 2023 Maths · Mathematics · Application of Integrals · medium

The area, in square units, of the region lying in the first quadrant and enclosed between the curve y=x^3 and the straight line y=x is

Single correct option

The area, in square units, of the region lying in the first quadrant and enclosed between the curve

y=x^3

and the straight line

y=x

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Answer: (B) $\dfrac14$

In the first quadrant the curves meet at

x=0

and

x=1

, and the line lies above the cubic. Area

=\int_0^1(x-x^3)dx=\dfrac12-\dfrac14=\dfrac14

. The value

\dfrac12

is only the area under the line.

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