`int_-1^1(x^100)dx` Evaluate the integral.

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Chapter 5, 5.3 - Problem 20 - 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 x^100 dx`

To evaluate this, apply the formula `int x^n dx = x^(n+1)/(n+1)` .

`= x^101/101 |_(-1)^1`

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

`= 1^101/101 - (-1)^101/101`

And, simplify it.

`=1/101+ 1/101`

`=2/101`

 

Therefore,  `int_(-1)^1 x^100 dx = 2/101` .

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