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JH
Numerade Educator

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Problem 7 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int_{-1}^1 \frac{e^{\arctan y}}{1 + y^2}\ dy $

Answer

$e^{\pi / 4}-e^{-\pi / 4}$

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Video Transcript

Let's do it. Use up for this one. Let's take you to be our tan. Why then, do you look so recall the distributed for the inverse hand function? Then, from there I could come back to this integral rewrite this. So that's just either the u and then this remaining piece over here. Let's just do it. So here, I don't need a denominator. You do you? So this corresponds to this. And then this corresponds to this Due to this over here, the last thing to do before we integrate is to find the new limits. So here, plug in negative one. And for why? So we have our ten negative one. That's negative. Pyro for and then similarly for the upper limit ten inverse. A positive one is positive power for So these are limits. So integrate that get you to the U. Here are your end points and then just subtract. And that's your final answer.