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Get Started Now- Intro Lesson4:13
- Lesson: 12:55
- Lesson: 24:53

The average value of a function is just the mean value theorem for integrals. In this lesson, we learn that we can find an area of a rectangle that is exactly the same as the area under the curve. Equating them together and algebraically manipulating the equation will give us the formula for the average value. We will be taking a look at some examples of using this formula, as well as using the formula to find the c value that is between a and b.

- Introduction
- 1.Find the average value of the function $f(x)=4+x-x^3$ on the interval [-2,3].
- 2.Given that $f(x)=4-x^2$, [-1,3]. Use the Mean Value Theorem for Integrals to find $c$ in [-2,3] such that $f_{average}= f(c)$

6.

Integral Applications

6.1

Average value of a function

6.2

Areas between curves

6.3

Area of polar curves

6.4

Volumes of solids with known cross-sections

6.5

Volumes of solids of revolution - Disc method

6.6

Volumes of solids of revolution - Shell method

6.7

Arc length and surface area of parametric equations

6.8

Arc length of polar curves

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