Question

Integral Calculation

Answer 1

Answer:

$\frac{4}{3(e^2+1)}$

Step-by-step explanation:

We want to evaluate:

$\int\limits^1_{-1} {\frac{x^2+1}{e^2+1} } \, dx$

This is the same as:

$\frac{2}{e^2+1} \int\limits^1_{0} {x^2+1} \, dx$

We integrate to obtain:

$\frac{2}{e^2+1} (\frac{x^3}{3}+x)|_0^1$

We evaluate to obtain:

$\frac{2}{e^2+1} (\frac{1^3}{3}+1)=\frac{4}{3(e^2+1)}$