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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 11

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 11

Answers (1)

Answer: \frac{\sin ^{2}x}{2}+c

Hint:  You must know about the integration rule of logarithm, sin and cos function.

Given :  \int e^{\log \sin x}.\cos x dx

Solution :

I=\int e^{\log \sin x}.\cos x dx

I=\int \sin x.\cos x dx                                                                      [\because e \log a =a]

Let \sin x =t      differentiate both sides, \left [ \frac{d}{dx}\sin x= \cos x \right ]

cos x \: dx=dt

\therefore I= \int t dt

   = \frac{t^{2}}{2}+c                                                                                               \left [ \int x^{n} dx= \frac{x^{n+1}}{n+1} \right ]

  = \frac{\sin ^{2}x}{2}+c

 

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