Presentation is loading. Please wait.

Presentation is loading. Please wait.

6/3/2016 Perkins AP Calculus AB Day 10 Section 4.4.

Published byFelicity Cameron Modified over 8 years ago

Similar presentations

Presentation on theme: "6/3/2016 Perkins AP Calculus AB Day 10 Section 4.4."— Presentation transcript:

1 6/3/2016 Perkins AP Calculus AB Day 10 Section 4.4

2 The Mean Value Theorem for Integrals Gives the average value of f(x) on [a,b].

3 1.Find the average value of on [1,4]. Then find where f(x) obtains this average value. This value is obtained when…

4 Using the 2 nd Fundamental Theorem of Calculus:

5 Second Fundamental Theorem of Calculus In order to use this shortcut we must have… a derivative… of an integral… whose lower bound is constant… and whose upper bound is a function of x.

6 Using the 2 nd Fundamental Theorem of Calculus: We don’t know how to integrate this function!

7 Perkins AP Calculus AB Day 10 Section 4.4

8 The Mean Value Theorem for Integrals

9 1.Find the average value of on [1,4]. Then find where f(x) obtains this average value.

10

11 Second Fundamental Theorem of Calculus

12

Download ppt "6/3/2016 Perkins AP Calculus AB Day 10 Section 4.4."

Similar presentations

Average Value and the 2 nd Fundamental Theorem. What is the area under the curve between 0 and 2? f(x)

Average Value and the 2 nd Fundamental Theorem. What is the area under the curve between 0 and 2? f(x)
Created by Jason L. Bradbury State Standard – 15.0b Students use the fundamental theorem of calculus to interpret integrals as antidervivatives. – 14.0.

Created by Jason L. Bradbury State Standard – 15.0b Students use the fundamental theorem of calculus to interpret integrals as antidervivatives. – 14.0.
4/30/2015 Perkins AP Calculus AB Day 4 Section 7.2.

4/30/2015 Perkins AP Calculus AB Day 4 Section 7.2.
Follow the link to the slide. Then click on the figure to play the animation. A Figure 5.1.8 Figure 5.1.9.

Follow the link to the slide. Then click on the figure to play the animation. A Figure Figure
5/16/2015 Perkins AP Calculus AB Day 5 Section 4.2.

5/16/2015 Perkins AP Calculus AB Day 5 Section 4.2.
5/19/2015 Perkins AP Calculus AB Day 7 Section 7.2.

5/19/2015 Perkins AP Calculus AB Day 7 Section 7.2.
Stokes’ Theorem Divergence Theorem

Stokes’ Theorem Divergence Theorem
1 Fundamental Theorem of Calculus Section 4.4. 2 The Fundamental Theorem of Calculus If a function f is continuous on the closed interval [a, b] and F.

1 Fundamental Theorem of Calculus Section The Fundamental Theorem of Calculus If a function f is continuous on the closed interval [a, b] and F.
The Fundamental Theorem of Calculus Inverse Operations.

The Fundamental Theorem of Calculus Inverse Operations.
5.4 The Fundamental Theorem. The Fundamental Theorem of Calculus, Part 1 If f is continuous on, then the function has a derivative at every point in,

5.4 The Fundamental Theorem. The Fundamental Theorem of Calculus, Part 1 If f is continuous on, then the function has a derivative at every point in,
Fundamental Theorems of Calculus 6.4. The First (second?) Fundamental Theorem of Calculus If f is continuous on, then the function has a derivative at.

Fundamental Theorems of Calculus 6.4. The First (second?) Fundamental Theorem of Calculus If f is continuous on, then the function has a derivative at.
Aim: What is the Fundamental Theorem of Calculus?

Aim: What is the Fundamental Theorem of Calculus?
Warm Up. 6.4 Fundamental Theorem of Calculus If you were being sent to a desert island and could take only one equation with you, might well be your.

Warm Up. 6.4 Fundamental Theorem of Calculus If you were being sent to a desert island and could take only one equation with you, might well be your.
4-3 DEFINITE INTEGRALS MS. BATTAGLIA – AP CALCULUS.

4-3 DEFINITE INTEGRALS MS. BATTAGLIA – AP CALCULUS.
Section 5.3 – The Definite Integral

Section 5.3 – The Definite Integral
Question from Test 1 Liquid drains into a tank at the rate 21e-3t units per minute. If the tank starts empty and can hold 6 units, at what time will it.

Question from Test 1 Liquid drains into a tank at the rate 21e-3t units per minute. If the tank starts empty and can hold 6 units, at what time will it.
5.c – The Fundamental Theorem of Calculus and Definite Integrals.

5.c – The Fundamental Theorem of Calculus and Definite Integrals.
Chapter 9 Theory of Differential and Integral Calculus Section 1 Differentiability of a Function Definition. Let y = f(x) be a function. The derivative.

Chapter 9 Theory of Differential and Integral Calculus Section 1 Differentiability of a Function Definition. Let y = f(x) be a function. The derivative.
Section 5.4a FUNDAMENTAL THEOREM OF CALCULUS. Deriving the Theorem Let Apply the definition of the derivative: Rule for Integrals!

Section 5.4a FUNDAMENTAL THEOREM OF CALCULUS. Deriving the Theorem Let Apply the definition of the derivative: Rule for Integrals!
AP Calculus Definite Integrals Review (sections 5.6-5.10)

AP Calculus Definite Integrals Review (sections )

Similar presentations

Ads by Google