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  • Provide Solution for RD Sharma Class 12 Chapter Indefinite Integrals Exercise 18.28 Question 9

Provide Solution for RD Sharma Class 12 Chapter Indefinite Integrals Exercise 18.28 Question 9

Answers (1)

Answer:-

2 x \sqrt{x^{2}-\frac{5}{4}}+\frac{5}{2} \log \left|x+\sqrt{x^{2}-\frac{5}{4}}\right|+c

Hint:-

Taking common 2 and then use the formula.

Given:-

\int \sqrt{4 x^{2}-5} d x

Solution:-

\begin{aligned} &=4 \int \sqrt{x^{2}-\left(\frac{\sqrt{5}}{2}\right)^{2}} d x \\\\ &=4\left[\frac{1}{2} x \sqrt{(x)^{2}-\frac{5}{4}}-\frac{1}{2} \times \frac{5}{4} \log \left[x+\sqrt{x^{2}-\frac{5}{4}}\right]+c\right] \end{aligned}

 

By using the formula

\begin{aligned} &\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 \\\\ &=2 x \sqrt{x^{2}-\frac{5}{4}}+\frac{5}{2} \log \left|x+\sqrt{x^{2}-\frac{5}{4}}\right|+c \end{aligned}

 

 

 

 

Posted by

infoexpert27

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