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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

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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}

 

 

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