The value of x x dx is : - Vidyadip

MCQ

The value of $\int\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$ is :

A
$2\cos\sqrt{\text{x}}+\text{C}$
B
$\sqrt{\frac{\cos\text{x}}{\text{x}}}+\text{C}$
C
$\sin\sqrt{\text{x}}+\text{C}$
✓
$2\sin\sqrt{\text{x}}+\text{C}$

✓

Answer

Correct option: D.

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

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

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