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  • Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 7

Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 7

Answers (1)

Answer:

2
Given:

\int_{0}^{\frac{\pi^{2}}{4}} \frac{\sin \sqrt{x}}{\sqrt{x}} d x

Hint:

Using \int \sin x\; dx

Explanation:  

Let

\begin{aligned} &I=\int_{0}^{\frac{\pi^{2}}{4}} \frac{\sin \sqrt{x}}{\sqrt{x}} d x \\\\ &\text { Put } \sqrt{x}=t \\\\ &\frac{1}{2 \sqrt{x}} d x=d t \\\\ &\frac{1}{\sqrt{x}} d x=2 d t \end{aligned}

\begin{aligned} &=\int_{0}^{\frac{\pi}{2}} \sin t \cdot 2 t\; d t \\\\ &=2\left[\frac{-\cos t}{1}\right]_{0}^{\frac{\pi}{2}} \end{aligned}

\begin{aligned} &=2\left[-\cos \frac{\pi}{2}+\cos 0\right] \\\\ &=2[0+1] \\\\ &=2 \end{aligned}

 

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infoexpert26

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