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  • Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.28 Question 7 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.28 Question 7 Maths Textbook Solution.

Answers (1)

Answer:-

\frac{1}{2} x \sqrt{9-x^{2}}+\frac{9}{2} \sin ^{-1} \frac{x}{3}+c

Hint:-

Using the formula

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

Given:-

\int \sqrt{9-x^{2}} d x

Solution:-

By using the formula

\begin{aligned} &=\int \sqrt{(3)^{2}-(x)^{2}} d x \\\\ &=\frac{1}{2} x \sqrt{9-x^{2}}+\frac{1}{2}(3)^{2} \sin ^{-1} \frac{x}{3}+c \end{aligned}

Using the formula

\begin{aligned} &\int \sqrt{a^{2}-x^{2}}=\frac{1}{2} x \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin ^{-1} \frac{x}{a}+c \\\\ &=\frac{1}{2} x \sqrt{9-x^{2}}+\frac{9}{2} \sin ^{-1} \frac{x}{3}+c \end{aligned}

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