NDA 2025 Maths · Mathematics · Definite Integrals · medium

The area enclosed between the curve y=f(x) and the x-axis from x=a to x=b is always equal to ∫a^bf(x) dx. 2. ∫a^bf(x) dx=∫a^bf(a+b-x) dx.

Single correct option

Consider the following statements:
1. The area enclosed between the curve

y=f(x)

and the

x

-axis from

x=a

x=b

is always equal to

\displaystyle\int_a^bf(x)\,dx

.
2.

\displaystyle\int_a^bf(x)\,dx=\int_a^bf(a+b-x)\,dx

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (B) $2$ only

Statement 1 is false: where the curve lies below the axis the integral is negative and the areas partly cancel, so the area needs

\int|f|

. Statement 2 is a standard property obtained by the substitution

x\to a+b-x

, so it is correct.

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