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  • Explain solution for RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 3 maths textbook solution.

Explain solution for  RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 3 maths textbook solution.

Answers (1)

Answer : \frac{\pi}{4}

Hints:- You must know the integration rules of trigonometric functions and its limits

Given : \int_{0}^{\pi / 2} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} d x

Solution : I=\int_{0}^{\pi / 2} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} d x                                     .....(1)

               I=\int \frac{\sqrt{\tan x}}{\sqrt{\tan x}+\sqrt{\cot x}}                                                 .....(2)

Adding (1) and (2)

              \begin{aligned} &2 I=\int_{0}^{\pi / 2} \frac{\sqrt{\tan x}+\sqrt{\cot x}}{\sqrt{\tan x}+\sqrt{\cot x}} d x \\ &2 I=\int_{0}^{\pi / 2} 1 \cdot d x \\ &2 I=[x]_{0}^{\pi / 2} \end{aligned}

             \begin{aligned} &I=\frac{1}{2} \times \frac{\pi}{2} \\ &=\frac{\pi}{4} \end{aligned}       

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