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Numerade Educator

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Problem 26 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int^5_{-5} e \,dx $

Answer

$$
10 e
$$

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Video Transcript

Okay, now we're going to answer the question. The integral off negative 5 to 5 e d. X Evaluate this thing. Okay, this is actually a trick question. A lot of people will associate E with the exponential function E to the X. Who's derivative is going to be e to the X and the integral is also a family of E to the X. Let's just not forget that are constant also comes into play. However, this is not a net exponential function. It doesn't have any X in the power. This is just eat. So it's almost the same as saying Find the integral off three approximately or 2.718 if you remember what this constant is approximately equal to. So this is simply a polynomial, a constant polynomial. So if you take the anti derivative, it'll be e times x, not eat to the X, okay, and then we can plug in negative 5 to 5. Of course, this is just a rectangle with height e where the base is going to be length 10 because that's a distance from negative 5 to 5. The answer is 10 e. So please do not fall for the job for this problem