Evaluate x x dx - Vidyadip

Question

Evaluate $\int\frac{\sin\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$

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Answer

Let $\text{I}=\int\frac{\sin\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$
Let $\sqrt{\text{x}}=\text{t}$
$\frac{1}{2\sqrt{\text{x}}}\text{dx}=\text{dt}$
$\therefore\ \text{I}=2\int\sin\text{t dt}$
$=-2\cos\text{t}+\text{C}$
$\text{I}=-2\cos\sqrt{\text{x}}+\text{C}$

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