MVT for Integrals and The Fundamental Theorem of Calculus FTC

Nov 20, 2014

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MVT for Integrals and The Fundamental Theorem of Calculus FTC.

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MVT for Integrals and The Fundamental Theorem of Calculus FTC

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MVT for Integrals and The Fundamental Theorem of Calculus FTC

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

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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.

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5.c – The Fundamental Theorem of Calculus and Definite Integrals

5.c – The Fundamental Theorem of Calculus and Definite Integrals. Examples. The definite integral of f ( x ) from x = a to x = b is denoted. f ( x ) is called the integrand , a the lower limit , and b the upper limit . . The First Fundamental Theorem of Calculus.

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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:

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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 ]. .

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Sections 4.2-4.4: Area, Definite Integrals, and The Fundamental Theorem of Calculus

Sections 4.2-4.4: Area, Definite Integrals, and The Fundamental Theorem of Calculus. Distance Traveled. A train moves along a track at a steady rate of 75 miles per hour from 3:00 A.M. to 8:00 A.M. What is the total distance traveled by the train?. Applying the well known formula:.

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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.

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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.

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§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.

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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.

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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.

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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

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5.3 The Fundamental Theorem of Calculus

5.3 The Fundamental Theorem of Calculus. The Fundamental Thm, Part 2:. If f is continuous on [ a , b ], then. where F  = f. Ex 1 : Evaluate the integral. Ex 2 : Find the area under the parabola y = 4 x 2  5 from  2 to 3. The Fundamental Thm, Part 1:. Let’s say….

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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 :

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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.

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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

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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.

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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

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4.4 The Fundamental Theorem of Calculus

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4.4 The Fundamental Theorem of Calculus

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.

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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.

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