Mathematics

Evaluate : $$\displaystyle\int \frac{\cos \sqrt{x}}{\sqrt{x}}dx.$$


ANSWER

$$\displaystyle 2\sin \sqrt{x}.$$


SOLUTION
Let $$ \displaystyle I=\int  \frac { \cos  \sqrt { x }  }{ \sqrt { x }  } dx$$

Put $$\sqrt { x } =t\Rightarrow \dfrac { 1 }{ 2\sqrt { \left( x \right)  }  } dx=dt$$

Therefore 

$$I=\displaystyle 2\int  \cos  tdt=2\sin  t=2\sin  \sqrt { x } $$
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Single Correct Medium Published on 17th 09, 2020
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