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in this video were going to work on some definite integral problems so lets jump right into it lets start with this example what is the antiderivative of x to the third evaluated from 2 to 4. how can we integrate x cubed well lets review some basics if you want to find the anti-derivative of x to the n its going to be x to the n plus 1 divided by n plus 1. so the antiderivative of x squared is x cubed divided by three the antiderivative of x to the fourth is x to the fifth divided by five and for x to the seventh is x to the eighth divided by eight so therefore if we wish to find the anti-derivative of x cubed its going to be x to the fourth divided by fourth but evaluate it from two to four so we need to plug in the top number first and then the number on the bottom so lets plug in 4. its going to be 4 to the fourth divided by 4 minus 2 to the fourth divided by 4. so what is four to the fourth power well for one thing we can cancel a four so this is going to be four to the th