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Name: Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.21 Question 6 Maths Textbook Solution.
Uploaded: Tue, 2021-08-03 22:04
Description: Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.21 Question 6 Maths Textbook Solution.

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#Revision Exercise (RE)

Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.21 Question 6 Maths Textbook Solution.

Answers (1)

Answer: $-\sqrt{8+x-x^{2}}+\frac{1}{2} \sin ^{-1}\left(\frac{2 x-1}{\sqrt{33}}\right)+c$

Given: $\int \frac{x}{\sqrt{8+x-x^{2}}} d x$

Hint: Simplify the given function

Solution:

$\begin{aligned} &I=\int \frac{x}{\sqrt{8+x-x^{2}}} d x \\ &I=-\frac{1}{2} \int \frac{-2 x+1-1}{\sqrt{8+x-x^{2}}} d x \\ &I=-\frac{1}{2} \int \frac{-2 x+1}{\sqrt{8+x-x^{2}}} d x+\frac{1}{2} \int \frac{1}{\sqrt{8+x-x^{2}}} d x \end{aligned}$