NDA 2020 Maths · Mathematics · Definite Integrals · medium

∫2^5(√ x)/(√ x+√(7-x)) dx is equal to

Single correct option

\displaystyle\int_2^5\dfrac{\sqrt x}{\sqrt x+\sqrt{7-x}}\,dx

is equal to

Show answer and solution

Answer: (B) $\dfrac32$

Use

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

with

a+b=7

. The integral

I

then equals the same integral with numerator

\sqrt{7-x}

. Adding the two forms,

2I=\displaystyle\int_2^51\,dx=3

, so

I=\dfrac32

. The value

3

2I

, the usual trap of stopping after the addition, and

\dfrac72

\dfrac{a+b}{2}

rather than

\dfrac{b-a}{2}

Original question written in the NDA 2020 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