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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This week in AP Calculus, we learned learned about definite integrals. An definite integral is an integral expressed as the difference between the values of the integral at specified upper and lower limits of the independent variable. Under the topic of finite sums, we first learned an approximation method for interpreting the area under a curve called the Rectangular Approximation Method (RAM). The rectangular approximation method is used to approximate the area by taking the areas of rectangles on a given interval with a certain sub-interval that are touching the curve and adding up their areas to get the area under the curve. There are three types of RAM, right rectangle approximation method (RRAM), middle rectangle approximation method (MRAM), and left rectangle approximation method (LRAM). RRAM is when the rectangles right edge is touching the curve, MRAM is when the middle of the rectangle is intersecting the curve and LRAM is when the left edge of the rectangle is touching the curve. One way to define RRAM, MRAM, and LRAM is by using Riemann Sums. Riemann Sums is an easier way to define the RAM and it is used to approximate the area under the curve as well as the length of the curve. In section 5.3, we learned about the rules for definite integrals as well as how to calculate the average value of an integral. |
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January 2018
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