Evaluate the following functions : x x d x - Vidyadip

Question

Evaluate the following functions : $\int \frac{\cos \sqrt{x}}{\sqrt{x}} \cdot d x $

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Answer

$\begin{aligned} &\text {Let } \mathrm{I}=\int \frac{\cos \sqrt{x}}{\sqrt{x}} \cdot d x \\ & \text { put } \sqrt{x}=t \\ & \therefore \frac{1}{2 \sqrt{x}} \cdot d x=1 \cdot d t \\ & \therefore \frac{1}{\sqrt{x}} \cdot d x=2 \cdot d t \\ & =2 \cdot \int \cos t \cdot d t \\ & =2 \cdot \sin t+c \\ & =2 \cdot \sin \sqrt{x}+c \\ & \end{aligned}$

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