The substitution rule, also known as u-substitution, is a technique used in calculus to simplify integrals by substituting a variable in the integral with a new variable.
The substitution rule is used to make integrals easier to solve by simplifying the expression and making it easier to integrate by using basic integration rules.
The substitution rule is typically used when the integral contains a complicated function within the integral or when the integral contains a function and its derivative.
No, the substitution rule can only be used for certain integrals where a substitution can be made to simplify the expression. It is not applicable to all integrals.
The process for using the substitution rule involves identifying the variable to be substituted, finding the derivative of the substituted variable, and then rewriting the integral using the substituted variable and its derivative. The integral can then be solved using basic integration rules.