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For example: calculate $\int^4_2 \tan^{-1} x \, dx$

If $\tan^{-1}(-1) = 3\pi /4$, then the final answer is $\frac{-\pi}{2}$. But if $\tan^{-1}(-1)= 7\pi /4$, then the final answer would be $\frac{3}{-4\pi}$. Which is it?

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The value of $\arctan$ is defined to lie within $(-\pi/2,\pi/2)$. Therefore the value should be $-\pi/4$.

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  • $\begingroup$ Ohh completely forgot about that haha, thank you $\endgroup$ – James Ronald Apr 16 at 23:57

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