Q60 / 150 · MHT CET 2020 (15 Oct Shift 1) · Mathematics

$\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x=$

  • A
    $\frac{1}{2} \cos \sqrt{x}+\mathrm{c}$
  • Correct answer
    B
    $2 \sin \sqrt{x}+\mathrm{c}$
  • C
    $\frac{1}{2} \sin \sqrt{x}+\mathrm{c}$
  • D
    $2 \cos \sqrt{x}+\mathrm{c}$

Solution

$\begin{aligned} \text { Let } I &=\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x \\ \text { Put } \sqrt{x} &=t \Rightarrow \frac{1}{2 \sqrt{x}} d x=d t \\ \therefore I &=\int \cos t(2) d t \\ &=2 \int \cos t d t=2 \sin t+c=2 \sin \sqrt{x}+c \end{aligned}$

Hence, the correct answer is option: 'B'.

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