NDA 2025 Maths · Mathematics · Application of Integrals · hard

The area of the region bounded by the curve y=x^3, the line y=8 and the y-axis is

Single correct option

The area of the region bounded by the curve

y=x^3

, the line

y=8

and the

y

-axis is

Show answer and solution

Answer: (A) $12$ square units

Integrate with respect to

y

x=y^{1/3}

, so the area is

\int_0^8y^{1/3}dy=\frac34\cdot8^{4/3}=\frac34\cdot16=12

. Equivalently, the rectangle

2\times8=16

minus

\int_0^2x^3dx=4

. The value

16

is the rectangle and

4

is the area below the curve.

Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake