Evaluate: x x d x - Vidyadip

Question

Evaluate: $\int \frac{\sin \sqrt{x}}{\sqrt{x}} d x$

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Answer

$\begin{aligned} & \text { Let } I=\int\left(\frac{\sin \sqrt{x}}{\sqrt{x}}\right) d x \\ & \text { Let } \sqrt{x}=t \\ & \frac{1}{\sqrt{x}}=\frac{d t}{d x} \\ & \frac{1}{\sqrt{x}} d x=2 d t \\ & \therefore I=2 \int \sin t d t \\ & =-2 \cos t+C \\ & =-2 \cos (\sqrt{x})+C\end{aligned}$

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