Mathematics

The value of $\displaystyle\int { \cfrac { \cos { \sqrt { x } } }{ \sqrt { x } } } dx$ is

$2\sin { \sqrt { x } } +C$

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

Let $t=\sin{\sqrt{x}}\Rightarrow\,dt=\dfrac{\cos{\sqrt{x}}}{2\sqrt{x}}dx$

$\Rightarrow\,2dt=\dfrac{\cos{\sqrt{x}}}{\sqrt{x}}dx$

Now,$\displaystyle\int{\dfrac{\cos{\sqrt{x}}}{\sqrt{x}}dx}$

$=\displaystyle\int{2dt}=2t+c$ ......where $c$ is the constant of integration

$=2\sin{\sqrt{x}}+c$ ...........where $t=\sin{\sqrt{x}}$

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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