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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 104 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 104 Maths Textbook Solution.

Answers (1)

Answer: \frac{3}{2} \sin ^{-1} x-\frac{x}{2} \sqrt{1-x^{2}}+c

Hint: to solve this equation we have to solve this by splitting the team

Given:

                      I=\int \frac{1+x^{2}}{\sqrt{1-x^{2}}} d x

Solution:

\operatorname{Let} I=\int \frac{2-\left(1-x^{2}\right)}{\sqrt{1-x^{2}}} d x

I=\int \frac{2}{\sqrt{1-x^{2}}} d x-\int \frac{1-x^{2}}{\sqrt{1-x^{2}}} d x

I=\int \frac{2}{\sqrt{1-x^{2}}} d x-\int \sqrt{1-x^{2}} d x

I=2 \sin ^{-1} x-\left[\frac{x}{2} \sqrt{1-x^{2}}+\frac{1}{2} \sin ^{-1} x\right]+c .

                      \left\{\int \frac{1}{\sqrt{a^{2}-x^{2}}} d x=\frac{1}{a} \sin ^{-1} \frac{x}{a} \& \int \sqrt{a^{2}-x^{2}} d x=\frac{a}{2} \sqrt{a^{2}-x^{2}}+\frac{1}{2} \sin ^{-1}\left(\frac{x}{a}\right)\right\}

I=2 \sin ^{-1} x-\frac{x}{2} \sqrt{1-x^{2}}-\frac{1}{2} \sin ^{-1} x+c

I=\frac{3}{2} \sin ^{-1} x-\frac{x}{2} \sqrt{1-x^{2}}+c 

 

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