This week to continue our study of finding the area under a curve we looked at Definite integrals and we revisited antiderivatives. As a class we have already kind of touched on antiderivatives in the past to supplement our derivative studies in chapter 3 with U substitution. This week we used antiderivatives in relation to definite integrals. The anti derivative is like the indefinite integral of the function. In order to find an integral you can use antiderivatives, by using the formula
Where F(x) in the antiderivative of f(x). During our study of definite integrals we also looked at finding the average of a function on a closed interval. We can do this by looking at the definition of the average value which multiplies the whole definite integral by one over b, the right bound of the interval, minus a, the left bound of the interval. When applied this definition is the basis of The Mean Value Theorem for Definite Integrals. Shout out to Pauls Online Math Notes for like the sixteenth week in a row for helping me to put this into words after not looking at it all weekend and forgetting everything from the lecture. http://tutorial.math.lamar.edu/Classes/CalcI/ComputingDefiniteIntegrals.aspx
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