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The Value of ∫ Cos √ X √ X D X is - Mathematics

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MCQ

The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is

Options

  • 2 cos \[\sqrt{x}\]

  • \[\sqrt{\frac{\cos x}{x}} + C\]

  • sin \[\sqrt{x} + C\]

  • 2 sin \[\sqrt{x} + C\]

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Solution

2 sin \[\sqrt{x} + C\]

 

\[\text{Let }I = \int\frac{\cos \sqrt{x}}{\sqrt{x}}dx\]
\[\text{Putting }\sqrt{x} = t\]
\[ \Rightarrow \frac{1}{2\sqrt{x}}dx = dt\]
\[ \Rightarrow \frac{dx}{\sqrt{x}} = 2dt\]
\[ \therefore I = 2\int\cos t \cdot dt\]
\[ = 2 \sin t + C\]
\[ = 2 \sin \sqrt{x} + C ..................\left(\because t = \sqrt{x} \right)\]

Concept: Methods of Integration: Integration by Substitution
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
MCQ | Q 13 | Page 200
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