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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 111 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 111 Maths Textbook Solution.

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Answer:I=x \sec ^{-1} \sqrt{x}-\sqrt{x-1}+C

Hint: to solve this equation we have to useByparts equation;

           Given: I=\int \sec ^{-1} \sqrt{x} d x

Solution: Let \sec ^{-1} \sqrt{x} \text { be the first function and } 1 \text { as the second function }

I=\sec ^{-1} \sqrt{x} \cdot x-\int \frac{1}{\sqrt{x} \sqrt{x-1} \cdot 2 \sqrt{x}} \ldots . . \text { Using Byparts }

I=x \sec ^{-1} \sqrt{x}-\frac{1}{2} \int(x-1)^{-1 / 2} d x

I=x \sec ^{-1} \sqrt{x}-\sqrt{x-1}+C

 

 

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