4.4 The Fundamental Theorem of Calculus

Jan 06, 2020

150 likes | 215 Views

4.4 The Fundamental Theorem of Calculus. Evaluating a Definite Integral. Evaluate each definite integral. A definite integral involving absolute value. Using the fundamental theorem to find area.

Share Presentation

Embed Code

Link

interval
definite integral
find area
fundamental theorem
interval 1
definite integral involving absolute

jshanta

Download Presentation

4.4 The Fundamental Theorem of Calculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

4.4 The Fundamental Theorem of Calculus
Evaluating a Definite Integral • Evaluate each definite integral.
A definite integral involving absolute value
Using the fundamental theorem to find area • Find the area of the region bounded by the graph , the x-axis, and the vertical lines x=0 and x=2.
Using Mean Value Theorem • Find the values of c guaranteed by the mean value theorem for integrals over the given interval.
Finding the Average Value of a Function • Find the average value of on the interval [1,4].
The Definite Integral as a Function • Evaluate the function at
Using the Second Fundamental Theorem of Calculus
Using the Second Fundamental Theorem of Calculus • Find the derivative of

THE FUNDAMENTAL THEOREM OF CALCULUS

THE FUNDAMENTAL THEOREM OF CALCULUS. The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus and integral calculus. DEFINITION. Example. A function is called an

663 views • 32 slides

The Fundamental Theorem of the Calculus

The Fundamental Theorem of the Calculus. Mike Thomas The University of Auckland. Overview. Why is the fundamental theorem of calculus (FTC) important?? Brief theory Using Geogebra to build understanding of the FTC Classroom materials?. Integration.

767 views • 36 slides

4.4 The Fundamental Theorem of Calculus

4.4 The Fundamental Theorem of Calculus. If a function is continuous on the closed interval [a, b], then. where F is any function that F’(x) = f(x) x in [a, b]. Examples. 1 – 0 = 1. Integration with Absolute Value. We need to rewrite the integral into two parts.

1.03k views • 9 slides

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus . Isaac Newton 1642 - 1727. 1702 portrait by Kneller The original is in the National Portrait Gallery in London. On 16 July 1730 in Mathematics. Alexander Pope (1688-1744) published the famous lines which were intended as an epitaph for Newton:

325 views • 18 slides

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus . Some books have the First and Second Fundamental Theorem of Calculus switched. They are switched in this PowerPoint, I will usually use our books rendition of the theorem. Fundamental Theorem of Calculus. Let f be a continuous function on [ a , b ]. .

409 views • 14 slides

Section 4.4 – The Fundamental Theorem of Calculus

Section 4.4 – The Fundamental Theorem of Calculus. The First Fundamental Theorem of Calculus. If f is continuous on the interval [ a , b ] and F is any function that satisfies F '( x ) = f ( x ) throughout this interval then. Alternative forms:. Example 1. Evaluate .

1.57k views • 41 slides

5.4 The fundamental theorem of calculus

5.4 The fundamental theorem of calculus. (Part 2 of the FTC in your book) If f is continuous on [ a, b ] and F is an antiderivative of f on [ a, b ], then. the fundamental theorem of calculus. ** F(b) – F(a) is often denoted as.

375 views • 14 slides

The First Fundamental Theorem of Calculus

The First Fundamental Theorem of Calculus. First Fundamental Theorem. Take the Antiderivative. Evaluate the Antiderivative at the Upper Bound. Evaluate the Antiderivative at the Lower Bound. Subtract the Lower Bound Value from the Upper Bound Value.

350 views • 17 slides

§12.5 The Fundamental Theorem of Calculus

§12.5 The Fundamental Theorem of Calculus. The student will learn about:. the definite integral,. the fundamental theorem of calculus,. and using definite integrals to find average values. Fundamental Theorem of Calculus.

540 views • 30 slides

5.3 The Fundamental Theorem of Calculus

INTEGRALS. 5.3 The Fundamental Theorem of Calculus. In this section, we will learn about: The Fundamental Theorem of Calculus and its significance. FUNDAMENTAL THEOREM OF CALCULUS. The Fundamental Theorem of Calculus (FTC) is appropriately named.

1.2k views • 74 slides

4.4 2 nd Fundamental Theorem of Calculus

4.4 2 nd Fundamental Theorem of Calculus. Variables of integration. F: function of x. Variable of integration. a=#. Variable of integration. a ,b =#s. Finding F(x). Find F as a function of x and evaluate at x=2,5,8 for. Answer. Integrate and evaluate. 2 nd FToC. Use 2 nd FToC.

228 views • 9 slides

The First Fundamental Theorem of Calculus

The First Fundamental Theorem of Calculus. First FTOC. ** Notice!! You do not have to include a “C” when you integrate f(x). Example Evaluating an Integral. Example. The Derivative of an Integral. Now let’s see some more examples / practice of definite integral problems.

905 views • 23 slides

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus . This power point presentation is created and written by Dr. Julia Arnold Using the 5 th edition of S. T. Tan’s text Applied Calculus. History:. Georg Friedrich Bernhard Riemann

312 views • 11 slides

4.4 Fundamental Theorem of Calculus Part 1

Photo by Vickie Kelly, 1998. Greg Kelly, Hanford High School, Richland, Washington. 4.4 Fundamental Theorem of Calculus Part 1. Morro Rock, California. Photo by Vickie Kelly, 1998. Greg Kelly, Hanford High School, Richland, Washington. 5.4 First Fundamental Theorem.

298 views • 7 slides

4.4 The Fundamental Theorem of Calculus

4.4 The Fundamental Theorem of Calculus. Essential Question : How are the integral & the derivative related?. The Fundamental Thm, Part 1:. If f is continuous on [ a , b ], then. where F  = f. Ex 1 : Find the area under the parabola y = x 2 from 0 to 1. Ex 2 :

277 views • 13 slides

Fundamental Theorem of Calculus

Fundamental Theorem of Calculus. Finally!. Objective…. To integrate using the Fundamental Thm of Calc. Pandora’s box…. Fundamental Thms. The Fundamental Theorem of Arithmetic: Any positive integer can be represented in exactly one way as a product of primes.

486 views • 20 slides

Ch 4.4 – The Fundamental Theorem of Calculus (day 2)

Ch 4.4 – The Fundamental Theorem of Calculus (day 2). Target Goals: Find the value of c guaranteed by the Mean Value Theorem for Integrals Find the average value of the function over an interval. Mean Value Theorem for Integrals.

240 views • 7 slides

THE FUNDAMENTAL THEOREM OF CALCULUS

THE FUNDAMENTAL THEOREM OF CALCULUS. Section 4.4. When you are done with your homework, you should be able to…. Evaluate a definite integral using the Fundamental Theorem of Calculus Understand and use the Mean Value Theorem for Integrals

382 views • 14 slides

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus. This One’s a Two- Parter ! FTC Part Two First Then FTC Part One. FTC: Part Two…First. If f is continuous on [ a, b ], and if F is any antiderivative of f on [ a, b ], then But we already knew that now didn’t we?!. FTC: Part One.

343 views • 13 slides

Fundamental Theorem of Calculus

The fundamental theorem of calculus is a theorem that links the concept of integrating a function with that differentiating a function. When the upper and the lower limit of an independent variable of the function or integrand is, its integration is described by definite integrals Read our full blog which help to understand the concept of Fundamental Theorem of Calculus – Infographic

54 views • 1 slides

4.4 The Fundamental Theorem of Calculus

168 views • 13 slides

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus. (Integral of a derivative over a region is related to values at the boundary). Dot Product: multiply components and add. Cross Product: determinant of matrix with unit vector. EM Fields.

407 views • 31 slides

More Related