Sometimes when evaluating a definite integral, you find one of the terms within your integral to either be 0 or infinity, which makes it invalid to evaluate. In that case, you can use improper integrals to evaluate the integral. You replace the bound that is giving you the problem with a variable, and evaluate the integral with the thinking that it approaches that value, but never approximately reaches it. This will allow you to further solve. Examples are below.
Steps: 1. Identify which bound is making your integral improper 2. Replace that bound with a variable, and place a limit notation in front of that integral as the variable approaches the real bound value 3. Evaluate the integral with any method that works (power, u-sub, by parts, trig sub, etc.) 4. Plug in the bounds and determine if the integral is equal to a constant or if it's equal to positive or negative infinity. It will converge if it goes to a constant and diverge otherwise.