Presentation on theme: "6.2 Integration by Substitution & Separable Differential Equations."— Presentation transcript:
6.2 Integration by Substitution & Separable Differential Equations
The chain rule allows us to differentiate a wide variety of functions, but we are able to find antiderivatives for only a limited range of functions. We can sometimes use substitution to rewrite functions in a form that we can integrate.
Example: The variable of integration must match the variable in the expression. Don’t forget to substitute the value for u back into the problem!
Example: One of the clues that we look for is if we can find a function and its derivative in the integrand. The derivative of is.Note that this only worked because of the 2x in the original. Many integrals can not be done by substitution.