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  4. The value of the definite integral (1/π) ∫ limits02 ( tan -1((x/2))/x2+4) d x is equal to

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Q. The value of the definite integral $\frac{1}{\pi} \int\limits_0^2 \frac{\tan ^{-1}\left(\frac{x}{2}\right)}{x^2+4} d x$ is equal to

Integrals

Solution:

Put $\tan ^{-1}\left(\frac{x}{2}\right)=t$ an proceed