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Numerade Educator

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Problem 45 Easy Difficulty

Use the result of Example 3 to evaluate $ \displaystyle \int^3_1 e^{x + 2} \, dx $.

Answer

$e^{5}-e^{3}$

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Video Transcript

Yeah, example here integrate the definite integral 1 to 3 of E to the X plus two. Given the fact that we've already worked the integral from 1 to 3 of E to the X is E cubed minus E. So we can rewrite this integral using properties of exponents. So this is the integral from 1 to 3 of E to the X E squared dx E squared is simply a constant. So this is E squared. The integral from 1 to 3 E to the X dx. That is precisely the result that you see right here. So this answer just turns into e squared E cubed minus E. Um you could factor one mori out of this and this is going to be what E cubed um E squared minus one or simply Each of the 5th minus E cubed. Mhm.