Question

Integral Calculation

What's the integral of:

`\frac{ {x}^(2) + 1}{ {e}^(2) + 1 }`
from -1 to 1 ?​

I know that it should be equal to 4/3, but how do we reach to that conclusion?

Answer 1

`(4)/(3(e^2+1))`

Explanation:

We want to evaluate:

`\int\limits^1_(-1) {(x^2+1)/(e^2+1) } \, dx`

This is the same as:

`(2)/(e^2+1) \int\limits^1_(0) {x^2+1} \, dx`

We integrate to obtain:

`(2)/(e^2+1) ((x^3)/(3)+x)|_0^1`

We evaluate to obtain:

`(2)/(e^2+1) ((1^3)/(3)+1)=(4)/(3(e^2+1))`