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  • Choose the correct answer in Exercises 10 to 11. Integral root of 1 + x^2 d x is equal to (A) (B) (C) (D)

Choose the correct answer in Exercises 10 to 11.

    Q10.    \int \sqrt{1+x^2}dx is equal to

                (A)    \frac{x}{2}\sqrt{1+x^2} + \frac{1}{2}\log\left |\left(x + \sqrt{1+x^2} \right )\right| +C

                (B)    \frac{2}{3}(1+x^2)^{\frac{3}{2}} + C

                (C)    \frac{2}{3}x(1+x^2)^{\frac{3}{2}} + C

                (D)    \frac{x^2}{2}\sqrt{1+x^2} + \frac{1}{2}x^2\log\left |x + \sqrt{1+x^2} \right| +C

Answers (1)

best_answer

As we know that, \int \sqrt{x^2+a^2}dx = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log|x+\sqrt{x^2+a^2}| +C

So, \int \sqrt{1+x^2}dx = \frac{x}{2}\sqrt{x^2+1}+\frac{1}{2}\log|x+\sqrt{x^2+1}| +C

Therefore the correct answer is A. 

 

Posted by

Divya Prakash Singh

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