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Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 13 Maths Textbook Solution.

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Answer:

2 \sin \sqrt{x}+C

Given:

\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x

Hint

Using \int \cos x d x

Explanation:

Let \mathrm{I}=\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x

        =\int \cos t .2 d t                                                                    \left[\text { Put } \sqrt{x}=t \Rightarrow \frac{1}{2 \sqrt{x}} d x=d t \Rightarrow \frac{d x}{\sqrt{x}}=2 d t\right]

        \begin{aligned} &=2 \int \cos t d t \\ &=2 \sin t+C \\ &=2 \sin \sqrt{x}+C \end{aligned}                                                                   \left[\because \int \cos x d x=\sin x+C\right]

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