This week in AP Calculus, the new topic that we learned about seemed oddly familiar. Back in trimester one, we learned about a topic called U-Substitution which was a strategy for anti-deriving a function. Just when we thought it was gone forever, it decided to make a comeback, like Brett Favre, and this time it was not much different than the first time around, also like Brett Favre. The only difference this time was that U-Substitution was applied to the fundamental theorem of calculus. The process for integrating with U-Substitution is this, first you start by choosing a "U", then you take the derivative of the U function and try to match it with the integral. To find the bounds for the new Integral, you plug in the original bounds of the integral to the u equation and then you get the new bounds. Next, you plug in the du (derivative of u) to the integral and then the fundamental theorem of calculus takes over. You antiderive the U function and then evaluate using the new bounds of the U function. After you contemplate, calculate, and evaluate, you get the value of the integral.
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January 2018
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