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  • Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise Revision Exercise question 52

Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise Revision Exercise question 52

Answers (1)

Answer:   \frac{}{}\frac{1}{2}

Hint: To use this equation, we use  \int_{0}^{a} f(x) d x   formula

Given:  \int_{2}^{3} \frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}} d x

Solution:

I=\int_{2}^{3} \frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}} d x     …………….  (1)

\begin{aligned} &I=\int_{2}^{3} \frac{\sqrt{5-x}}{\sqrt{5-(5-x)}+\sqrt{5-x}} d x \\ & \end{aligned}

I=\int_{2}^{3} \frac{\sqrt{5-x}}{\sqrt{x}+\sqrt{5-x}} d x    ……………… (2)

By adding (1) and (2)

\begin{aligned} &2 I=\int_{2}^{3} \frac{\sqrt{x}+\sqrt{5-x}}{\sqrt{x}+\sqrt{5-x}} d x \\ & \end{aligned}

2 I=\int_{2}^{3} d x \Rightarrow 2 I=[x]_{3}^{2} \\

2 I=[3-2] \\

I=\frac{1}{2}

 

 

Posted by

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