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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.6 Question 6

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.6 Question 6

Answers (1)

Answer:  

\frac{1}{2}(\mathrm{x}+\sin \mathrm{x})+\mathrm{c}

Hint:

2 \cos ^{2} x / 2=1+\cos x

Given:

let    \mathrm{I}=\int \cos ^{2} \frac{\mathrm{x}}{2} \mathrm{dx}
Solution:

\begin{aligned} &\mathrm{I}=\int \cos ^{2} \frac{\mathrm{x}}{2} \mathrm{dx} \\ &\mathrm{I}=\frac{1}{2} \int 2 \cos ^{2} \frac{\mathrm{x}}{2} \mathrm{dx} \\ &\mathrm{I}=\frac{1}{2} \int(1+\cos \mathrm{x}) \mathrm{dx} \end{aligned}

\begin{aligned} &\mathrm{I}=\frac{1}{2} \int \mathrm{d} \mathrm{x}+\frac{1}{2} \int \cos \mathrm{x} \mathrm{d} \mathrm{x} \\ &=\frac{1}{2}(\mathrm{x})+\frac{1}{2} \cdot \sin \mathrm{x}+\mathrm{c} \\ &=\frac{1}{2}(\mathrm{x}+\sin \mathrm{x})+\mathrm{c} \end{aligned}

 

So the answer is   =\frac{1}{2}(\mathrm{x}+\sin \mathrm{x})+\mathrm{c}

 

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