MHT CET · Maths · Indefinite Integration
\(\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x=\)
- A \(\frac{1}{2} \cos \sqrt{x}+\mathrm{c}\)
- B \(2 \sin \sqrt{x}+\mathrm{c}\)
- C \(\frac{1}{2} \sin \sqrt{x}+\mathrm{c}\)
- D \(2 \cos \sqrt{x}+\mathrm{c}\)
Answer & Solution
Correct Answer
(B) \(2 \sin \sqrt{x}+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text { Let } I &=\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x \\ \text { Put } \sqrt{x} &=t \Rightarrow \frac{1}{2 \sqrt{x}} d x=d t \\ \therefore I &=\int \cos t(2) d t \\ &=2 \int \cos t d t=2 \sin t+c=2 \sin \sqrt{x}+c \end{aligned}\)
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