September 10, 2009
No CommentsHow to Solve an Integration Problem by Substitution
Description
This video shows an example of how to solve the same problem with and without substitution, to express how much easier substitution is. This video provides several example problems with clear explanations and solutions for each one.
Overview
The substitution rule comes in very useful no matter how you are trying to solve an integral. When you are presented with something that looks like you may need the chain rule to solve it, or you are presented with a polynomial term in the denominator of your integral, then you can use u-substitution. It is called that because the variable u is the most common one used. Once you have chosen a value for u, find the derivative and write it as du/dx = n, with n being the number value of du/dx. Now, move the du over so that you are left with a value for dx. Now skip back to your original problem. Once you replace a term with u, you are normally left with a common integral, which is easy to solve. Multiply that by dx, just like in the problem. dx will be expressed as what you just solved for. If this is a multiplication problem, move all numbers to the outside and leave yourself with just the variables. Now you should be able to solve this like a normal integration problem.
