`int_-1^1(e^(u + 1))du` Evaluate the integral.

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Chapter 5, 5.3 - Problem 41 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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lemjay | High School Teacher | (Level 3) Senior Educator

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`int_(-1)^1 e^(u+1)du`

To evaluate this, apply the formula `int e^x dx = e^x` .

`= e^(u+1) |_(-1)^1`

Then, plug-in the limits of the integral as follows `F(x) =int_a^b f(x)dx=F(b)-F(a)` .

`=e^(1+1)-e^(-1+1)`

`=e^2-e^0`

`=e^2-1`

 

Therefore,  `int_(-1)^1 e^(u+1)du=e^2-1` .

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