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  4. Evaluate: ∫ limits- 11 log(x + √x2 + 1)dx

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Q. Evaluate : $\int \limits_{- 1}^{1}\log\left(x + \sqrt{x^{2} + 1}\right)dx$

NTA AbhyasNTA Abhyas 2022

Solution:

as $\log\left(x + \sqrt{1 + x^{2}}\right)$ is an odd function.
So $\int\limits_{-1}^{1} \log \left(x+\sqrt{1+x^{2}}\right) d x=0$