Presentation is loading. Please wait.

Presentation is loading. Please wait.

Wednesday, April 20, 2016MAT 145. Wednesday, April 20, 2016MAT 145.

Published byWinifred Berry Modified over 8 years ago

Similar presentations

Presentation on theme: "Wednesday, April 20, 2016MAT 145. Wednesday, April 20, 2016MAT 145."— Presentation transcript:

1 Wednesday, April 20, 2016MAT 145

2 Wednesday, April 20, 2016MAT 145

3 Wednesday, April 20, 2016MAT 145

4 Wednesday, April 20, 2016MAT 145 Riemann Sum Applet

5 Wednesday, April 20, 2016MAT 145 The first three methods build RECTANGLES on each subinterval and the fourth builds TRAPEZOIDS on each subinterval. In all cases, the lowercase letter k indicates the number of subintervals.

6 Wednesday, April 20, 2016MAT 145 Here is the velocity graph of a braking car. How far did the car travel during this 6-second brake application?

7 Wednesday, April 20, 2016MAT 145 Let g(x) = sin(x). Show a calculator graph of g(x) using window dimensions of [-1,4] on x and [-1.25,1.25] on y. Now calculate. Label your antiderivative G(x). Next, evaluate your antiderivative, G(x), when x = π and when x = π / 2. Finally, calculate G(π) – G( π / 2 ).

8 Wednesday, April 20, 2016MAT 145 This is called a definite integral. It includes lower bounds and upper bounds that represent boundary values of an x-axis interval. upper limit of integration lower limit of integration integrand differential

9 Wednesday, April 20, 2016MAT 145 Use the graph of y = f(x) shown here to express the value of each integral in terms of accumulated area.

10 MAT 145Wednesday, April 20, 2016

11 MAT 145

12 Wednesday, April 20, 2016MAT 145

13 Wednesday, April 20, 2016MAT 145

14 Wednesday, April 20, 2016MAT 145

15 Wednesday, April 20, 2016

16 MAT 145Wednesday, April 20, 2016

17 MAT 145

18 Wednesday, April 20, 2016MAT 145

Download ppt "Wednesday, April 20, 2016MAT 145. Wednesday, April 20, 2016MAT 145."

Similar presentations

Section 8.5 Riemann Sums and the Definite Integral.

Section 8.5 Riemann Sums and the Definite Integral.
Riemann Sums. Objectives Students will be able to Calculate the area under a graph using approximation with rectangles. Calculate the area under a graph.

Riemann Sums. Objectives Students will be able to Calculate the area under a graph using approximation with rectangles. Calculate the area under a graph.
Area Between Two Curves

Area Between Two Curves
Area Between Two Curves

Area Between Two Curves
Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.

Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.
Chapter 6 The Integral Sections 6.1, 6.2, and 6.3

Chapter 6 The Integral Sections 6.1, 6.2, and 6.3
5.2 Definite Integrals Greg Kelly, Hanford High School, Richland, Washington.

5.2 Definite Integrals Greg Kelly, Hanford High School, Richland, Washington.
5.2 Definite Integrals Quick Review Quick Review Solutions.

5.2 Definite Integrals Quick Review Quick Review Solutions.
The First Fundamental Theorem of Calculus. First Fundamental Theorem Take the Antiderivative. Evaluate the Antiderivative at the Upper Bound. Evaluate.

The First Fundamental Theorem of Calculus. First Fundamental Theorem Take the Antiderivative. Evaluate the Antiderivative at the Upper Bound. Evaluate.
Definition: the definite integral of f from a to b is provided that this limit exists. If it does exist, we say that is f integrable on [a,b] Sec 5.2:

Definition: the definite integral of f from a to b is provided that this limit exists. If it does exist, we say that is f integrable on [a,b] Sec 5.2:
The Integral chapter 5 The Indefinite Integral Substitution The Definite Integral As a Sum The Definite Integral As Area The Definite Integral: The Fundamental.

The Integral chapter 5 The Indefinite Integral Substitution The Definite Integral As a Sum The Definite Integral As Area The Definite Integral: The Fundamental.
David Loomis. is defined informally to be the signed area of the region in the xy-plane bounded by the graph of ƒ, the x- axis, and the vertical lines.

David Loomis. is defined informally to be the signed area of the region in the xy-plane bounded by the graph of ƒ, the x- axis, and the vertical lines.
Section 7.2a Area between curves.

Section 7.2a Area between curves.
6.3 Definite Integrals and the Fundamental Theorem.

6.3 Definite Integrals and the Fundamental Theorem.
Introduction to integrals Integral, like limit and derivative, is another important concept in calculus Integral is the inverse of differentiation in some.

Introduction to integrals Integral, like limit and derivative, is another important concept in calculus Integral is the inverse of differentiation in some.
5.c – The Fundamental Theorem of Calculus and Definite Integrals.

5.c – The Fundamental Theorem of Calculus and Definite Integrals.
First Fundamental Theorem of Calculus Greg Kelly, Hanford High School, Richland, Washington.

First Fundamental Theorem of Calculus Greg Kelly, Hanford High School, Richland, Washington.
7.4: The Fundamental Theorem of Calculus Objectives: To use the FTC to evaluate definite integrals To calculate total area under a curve using FTC and.

7.4: The Fundamental Theorem of Calculus Objectives: To use the FTC to evaluate definite integrals To calculate total area under a curve using FTC and.
MAT 1235 Calculus II 4.1, 4.2 Part I The Definite Integral

MAT 1235 Calculus II 4.1, 4.2 Part I The Definite Integral
5.2 Definite Integrals.

5.2 Definite Integrals.

Similar presentations

Ads by Google