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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 37

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 37        

Answers (1)

Answer: \frac{x}{2} \sqrt{x^{2}-9}-\frac{9}{2} \log \left|x+\sqrt{x^{2}-9}\right|+c

Given: \int \sqrt{x^{2}-9}dx

Solution:

\begin{aligned} &\int \sqrt{x^{2}-9} d x \\ &I=\int \sqrt{x^{2}-a^{2}} d x=\int \sqrt{x^{2}-3^{2}} d x \quad\left[\int \sqrt{x^{2}-a^{2}} d x=\frac{x}{2} \sqrt{x^{2}-a^{2}}-\frac{a^{2}}{2} \log \left|x+\sqrt{x^{2}-a^{2}}\right|+c\right] \end{aligned}

Given by

\therefore I=\frac{x}{2} \sqrt{x^{2}-9}-\frac{9}{2} \log \left|x+\sqrt{x^{2}-9}\right|+c

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