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  • Choose the correct answer. The anti derivative of equals (Q21)

Q21  Choose the correct answer 
         The anti derivative of \left ( \sqrt x + 1/ \sqrt x \right )  equals 

A) \frac{1}{3}x ^{1/3} + 2 x ^{1/2}+ C \\\\ B) \frac{2}{3}x ^{2/3} + \frac{1}{2}x ^{2}+ C \\\\ C ) \frac{2}{3}x ^{3/2} + 2 x ^{1/2}+ C\\\\ D) \frac{3}{2}x ^{3/2} + \frac{1}{2} x ^{1/2}+ C

Answers (1)

best_answer

Given to find the anti derivative or integral of \left ( \sqrt x + 1/ \sqrt x \right );

\int \left ( \sqrt x + 1/ \sqrt x \right )\ dx

\int x^{\frac{1}{2}}\ dx + \int x^{-\frac{1}{2}}\ dx

= \frac{x^{\frac{3}{2}}}{\frac{3}{2}} + \frac{x^{\frac{1}{2}}}{\frac{1}{2}}+C

= \frac{2}{3}x^{\frac{3}{2}} + 2x^{\frac{1}{2}} +C, where C is any constant value.

Hence the correct option is (C).

Posted by

Divya Prakash Singh

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