### Home > CALC > Chapter 11 > Lesson 11.2.4 > Problem 11-83

11-83.

Use integration by parts.

Let *f* = *x*^{2} and *dg* = *e*^{–}* ^{x}*.

Use substitution.

Let *u* = *x*^{2}.

You should recognize the integrand as the derivative of an inverse trigonometric function.

This is an improper integral, so a limit will need to be used to evaluate it.

The symmetry of the graph can also be used to evaluate the integral.

Review the first Fundamental Theorem of Calculus.