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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.6 Question 7

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.6 Question 7

Answers (1)

Answer:  

\frac{\mathrm{x}}{2}+\frac{\sin 2 \mathrm{nx}}{4 \mathrm{n}}+\mathrm{c}

Hint:

\cos 2 x=2 \cos ^{2} x-1

Given:

Let  \mathrm{I}=\int \cos ^{2} \mathrm{n} \mathrm{xdx}
Solution:

\begin{aligned} &\mathrm{I}=\int \cos ^{2} \mathrm{n} \mathrm{xdx} \\ &=\frac{1}{2} \int(1+\cos 2 \mathrm{nx}) \mathrm{dx} \\ &=\frac{1}{2}\left[\mathrm{x}+\frac{\sin 2 \mathrm{n} \mathrm{x}}{2 \mathrm{n}}\right]+\mathrm{c} \\ &=\frac{\mathrm{x}}{2}+\frac{\sin 2 \mathrm{nx}}{4 \mathrm{n}}+\mathrm{c} \end{aligned}

So the answer is  =\frac{\mathrm{x}}{2}+\frac{\sin 2 \mathrm{nx}}{4 \mathrm{n}}+\mathrm{c}

 

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