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JH
Numerade Educator

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Problem 18 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int_1^4 \frac{e^{\sqrt{t}}}{\sqrt{t}}\ dt $

Answer

$2 e^{2}-2 e$

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Video Transcript

Let's use a U substitution for this animal. Take you to be square. Rarity then do you one over two times a radical T or licious? Multiply that two over and we get DT over square of T. And that's precisely what we see over here in the original problem. So let's go ahead and rewrite this integral in terms of our new variable. So let's watch out for those limits of integration, we have a one there, so t equals one so plunged it into this equation. T equals one, so you equals one. So our lower limit will still be one. Now, check that upper limit too. So here t equals four. So you was too. So this is our new upper limit and our new variable now and then we just have e to the u Do you either The U accounts for this term up here and then, as we mentioned, do you and we forgot Forgot the too. So let me put that to our here so that this to do, you will account for the remaining part dt over the radical and and now just generate this. So that's just to eat the you wanted to. So to ease where minus to eat. And then there's you can factor a few if you must take out to you a minus one, and that's a final answer.