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प्रश्न
Evaluate:\[\int\frac{\sin \sqrt{x}}{\sqrt{x}} \text{ dx }\]
उत्तर
\[\text{ Let I } = \int\frac{\sin\sqrt{x}}{\sqrt{x}} dx\]
\[\text{ Let }\sqrt{x} = t\]
\[ \Rightarrow \frac{1}{2\sqrt{x}}dx = dt\]
\[ \Rightarrow \frac{dx}{\sqrt{x}} = 2 dt\]
\[\text{ Putting }\sqrt{x} = t \text{ and }\frac{dx}{\sqrt{x}} = 2 \text{ dt , we get} \]
\[ \therefore I = 2\int\text{ sin t dt}\]
\[ = - 2 \text{ cos t} + C \left( \because t = \sqrt{x} \right)\]
\[ = - 2 \cos \sqrt{x} + C\]
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