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  • need solution for rd sharma maths class 12 chapter Indefinite integrals exercise 18.1 question 1 sub question (vi)

need solution for rd sharma maths class 12 chapter Indefinite integrals exercise 18.1 question 1 sub question (vi)

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best_answer

Answer: 3\sqrt[3]{x}+c

Hint: Use the formula of \int {x^{n}}dx

Given: \int \frac{1}{\sqrt[3]{x^{2}}}dx

Solution: \int \frac{1}{\sqrt[3]{x^{2}}}dx=\int \frac{1}{x^{\frac{2}{3}}}dx

                =\int x^{\frac{-2}{3}}dx

                =\frac{x^{\frac{-2}{3}+1}}{\frac{-2}{3}+1}+c                                 \left ( \because \int x^{n}dx=\frac{x^{n+1}}{n+1}+c \right )

                =\frac{x^{\frac{1}{3}}}{\frac{1}{3}}+c

                =3\sqrt[3]{x}+c

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