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Analogy: Say you have a sheet of paper. You stack another piece of paper on top of that sheet. You continue doing this until you have a very thick, voluminous rectangular prism composed of many sheets of paper. In the same way, in volume using cross sections, we sum up the prisms that make up…

This is looking at the area between two functions by: ∫upper function – ∫lower function Area Between Two Curves (cr: Organic Chem Tutor)

This is the start of our APPLICATIONS of integrals section! Here you will be looking at two different areas a function can create with the x-axis and adding them up. Note: In previous chapters you may have seen area like: which would have cancelled out and = 0. HOWEVER, with signed area, we take the…

The derivative of an integral is the function, under the terms that the limit is a constant and a variable (x). Therefore “integrate” by using FTC pt.2 then use FTC pt1 to plug in the limits. If the variable is not x (ex. x²⁰) then we will have to integrate normally and use FTC. Finding…

This is similar to 3.8, only we are also utilizing Fundamental Theorem of Calculus as well when solving these. U-Substitution with Definite Integrals (cr: Khan Academy)

Recall using chain rule in the derivatives unit. You may have used the “u” substitution method where you set a function equal to “u” then substitute that function back in later in the problem. The main objective of this “u” substitution in this integral is to have the “u” function’s derivative’s be another function in…

Used in solving definite integrals by 1) anti-deriving 2) looking at the 2+ limits to use FTC 3) solving. This is useful in all application of integrals as you will be looking at complex area and volume questions. NOTE: unlike the indefinite integrals, the constant “c” is redundant here and will not be used. Introduction…

Here we look at Integrals that have no stated start and end, indefinite. These Integrals require you to include the constant “c” when integrating. You can solve these either by basic area formulas or anti-deriving. Indefinite Integrals (cr: Organic Chemistry Tutor) NOTE: you will be learning how to solve more complex integrals (definite and indefinite)…

Definite Integrals have a clear start and end (hence, “defined”). You can solve these using common area formulas or with fundamental theorem (1)– you will learn this in lesson 3.7! Definite Integrals using common area formulas (cr: Khan Academy) Definite Integrals Properties (cr: Khan Academy) https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-6/a/definite-integrals-properties-review Note: These properties are for DEFINITE integrals ONLY! Do…

Rectangular Approximation: Finding the area under the curve utilizing a given amount of rectangles, then choosing the points on those rectangle corners (left or right) that touch the curve. The more rectangles, the more accurate the approximation. Riemann sums: Finding the area under the curve using an INFINITE amount of rectangles– therefore most accurate (note:…