Properties of the Definite Integral

Aug 09, 2014

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Properties of the Definite Integral. 1:. 2:. 3:. 4:. 5:. 6:. 7:. 8:. 9:. 10:. 11:. 12:.

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Properties of the Definite Integral

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Properties of the Definite Integral 1: 2: 3: 4: 5: 6:
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8: 9: 10: 11:
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Area and the Definite Integral

Area and the Definite Integral. Tidewater Community College Mr. Joyner, Dr. Julia Arnold and Ms. Shirley Brown using Tan’s 5th edition Applied Calculus for the managerial , life, and social sciences text. Area and the Definite Integral.

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To approximate the definite integral

Numerical integration is the process of approximating a definite integral using well-chosen sums of function values. It is needed when we cannot find an antiderivative explicitly, as in the case of the Gaussian function. To approximate the definite integral.

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The Definite Integral

The Definite Integral. Riemann Sums. Sigma notation enables us to express a large sum in compact form. Riemann Sums. LRAM, MRAM,and RRAM are examples of Riemann sums S n =

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Chapter 5 – The Definite Integral

Chapter 5 – The Definite Integral. 5.1 Estimating with Finite Sums. Example Finding Distance Traveled when Velocity Varies. LRAM, MRAM, and RRAM approximations to the area under the graph of y=x 2 from x= 0 to x= 3. p.270 (1-19, 26, 27). 5.2 Definite Integrals.

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5.2: Definite Integral

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Definite Integral

Definite Integral. Two main points of view: Integral as (signed) area under curve Integral as antiderivative Riemann integral. Area Under Curves. Find area under curve between x=a and x=b by taking limits: First subdivide [a,b] into n equal subintervals

616 views • 18 slides

Riemann sums, the definite integral, integral as area

Riemann sums, the definite integral, integral as area. Section 5.2a. First, we need a reminder of sigma notation:. How do we evaluate :. …and what happens if an “infinity” symbol appears above the sigma???.  The terms go on indefinitely!!!. LRAM, MRAM, and RRAM are all examples of

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The Definite Integral

The Definite Integral. Finding area of polygonal regions can be accomplished using area formulas for rectangles and triangles. Finding area bounded by a curve is more challenging. Consider that the area inside a circle is the same as the area of an inscribed n-gon where n is infinitely large.

555 views • 25 slides

The definite integral

denotes the difference in value of f ( x ) between x = a and x = b . The definite integral. If . Then . In other words. Notationally we write. Example Evaluate ( i ) (ii) (iii) (iv) (v) (vi). y. Example The Line drawn below is of y = 2 x – 4

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The Definite Integral

The Definite Integral. Section 6.6. The Definite Integral. If a function f is continuous on an interval [ a,b ], then f is integrable on [ a,b ], and the net signed area A between the graph of f and the interval [ a,b ] is

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The Definite Integral

The Definite Integral. Section 6.6. Fundamental Theorem of Calculus. If f is continuous on [ a,b ] and F is any anti-derivative of f on [ a,b ], then. Fundamental Theorem of Calculus. If f is continuous on [ a,b ] and F is any anti-derivative of f on [ a,b ], then.

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4010-Properties of the Definite Integral (5.3)

4010-Properties of the Definite Integral (5.3). BC Calculus. Properties of Definite Integrals. Think rectangles Distance. A) B) C) D). f (x). a dx b. Properties of Definite Integrals. Think rectangles Distance. a c b. E) NOTE : Same Interval.

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Applications Of The Definite Integral

Applications Of The Definite Integral. The Area under the curve of a function. The area between two curves. The Volume of the Solid of revolution. Applications of the Definite Integral.

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The Definite Integral

The Definite Integral. When we find the area under a curve by adding rectangles, the answer is called a Rieman sum. The width of a rectangle is called a subinterval. The entire interval is called the partition. subinterval. partition. Subintervals do not all have to be the same size.

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Area and the Definite Integral

Area and the Definite Integral. Lesson 7.3A. a. b. The Area Under a Curve. Divide the area under the curve on the interval [a,b] into n equal segments Each "rectangle" has height f(x i ) Each width is x The area if the i th rectangle is f(x i ) • x We sum the areas. •.

264 views • 11 slides

The Definite Integral

The Definite Integral. Section 14.3. Definite integral. As the number of integrals increase while doing the Riemann sum, the answer becomes more accurate. The limit of the Riemann Sum is called the definite integral of f from a to b, written:. Example 1.

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Properties of Definite Integrals

Properties of Definite Integrals. Objectives. Students will be able to Calculate a definite integral using the properties of definite integrals. Calculate the area between a curve and the x -axis over a given interval. Use definite integrals to application problems.

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Chapter 6 The Definite Integral

Chapter 6 The Definite Integral. § 6.1. Antidifferentiation. Antidifferentiation. Finding Antiderivatives. EXAMPLE. Find all antiderivatives of the given function. Theorems of Antidifferentiation. The Indefinite Integral. Rules of Integration. Finding Antiderivatives. EXAMPLE.

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Properties of Definite Integrals

Properties of Definite Integrals. 6.3. Order of Integration. Zero. Constant Multiple. Sum and Difference. Additivity. Intervals can be added (or subtracted.). Integrals can be added and subtracted. Max-Min Inequality. Domination. Rules for Definite Integrals.

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6.5 The Definite Integral

6.5 The Definite Integral. In our definition of net signed area, we assumed that for each positive number n, the Interval [a, b] was subdivided into n subintervals of equal length to create bases for the approximating rectangles. For some functions, it may be more convienct to use

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Section 5.2 The Definite Integral

Section 5.2 The Definite Integral. AP Calculus November 19, 2009 Berkley High School, D1B1 todd1@toddfadoir.com. Summary. We learned that we can find the exact area on the interval [a,b] under a curve by taking the following limit…. The Riemann Sum.

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The Definite Integral

The Definite Integral. In this handout: Riemann sum Definition of a definite integral Properties of the definite integral. | P |. a = x 0. x 1. x 2. x n -1. x n =b. Riemann Sum.

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