Question

State the Substitution Rule. In practice how do you use it?

Short answer

The Substitution Rule states that: \(\int {f(g(x)){g^'}(x)dx = \int {f(u)du} } \)

Step-by-step solution

Step 1: Definition of Substitution Rule 

A principle in logic specifying what expressions may be substituted for one another.

Step 2: Assumptions and notations with Substitution definition

The substitution rule states that:

If u = g(x) is a differentiable function, then

\(\int {f(g(x)){g^'}(x)dx = \int {f(u)du} } \)

We use the substitution rule because it makes the integral easier to evaluate.