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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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