'Riemann sums' diaporamas de présentation

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Riemann Sums

Riemann Sums. Integral Properties. Indefinite Integrals. Integration by Substitution. Definite Integrals. $100. $100. $100. $100. $100. $200. $200. $200. $200. $200. $300. $300. $300. $300. $300. $400. $400. $400. $400. $400. $500. $500. $500. $500. $500.

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Drill: Evaluate each sum

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RIEMANN SUMS REVISITED

RIEMANN SUMS REVISITED. Integration (actually calculus ) is a very powerful tool, it gives us power to answer questions that the Greeks struggled with unsuccessfully (as did pre-calculus Mathematicians) for a very long time.

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The Integral And The Area Under A Curve

The Integral And The Area Under A Curve. How do we find the area between a curve and the x- axis from x = a to x = b ?. We could approximate it with rectangles:. We could use more than one rectangle to approximate the area.

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5.2 Definite Integrals

5.2 Definite Integrals. In this section we move beyond finite sums to see what happens in the limit, as the terms become infinitely small and their number infinitely large. Sigma notation enables us to express a large sum in compact form:. Definite Integrals.

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6.4 Integration with tables and computer algebra systems 6.5 Approximate Integration

6.4 Integration with tables and computer algebra systems 6.5 Approximate Integration. Tables of Integrals. A table of 120 integrals, categorized by form, is provided on the References Pages at the back of the book. References to more extensive tables are given in the textbook.

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Riemann Sums

Riemann Sums. Approximating Area. One of the classical ways of thinking of an area under a curve is to graph the function and then approximate the area by drawing rectangular or trapezoidal regions under the curve (or nearly so). .

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4.3 Riemann Sums and Definite Integrals

4.3 Riemann Sums and Definite Integrals. Objectives. Understand the definition of a Riemann sum. Evaluate a definite integral using limits. Evaluate a definite integral using properties of definite integrals. Riemann Sums.

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THE POWER OF ADDING AND MULTIPLYING

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Riemann Sums

Riemann Sums. Width of partition:. Adds the rectangles, where n is the number of partitions (rectangles). Height of rectangle for each of the x-values in the interval. What is a Riemann Sum?. Takes approximating the area under a curve with rectangles to the next level LOOKS LIKE:.

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Section 5.6: Approximating Sums

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Working With Triple Integrals

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4.3 Riemann Sums and Definite Integrals

4.3 Riemann Sums and Definite Integrals. HW: pg 271 1-10 (all) 12-20 (even). 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.

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MATH 2221

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Midpoint and Trapezoidal Rules

Midpoint and Trapezoidal Rules. Approximating Integrals. There are some cases when it is impossible to find the definite integral They can be approximated by using types of Riemann sums. Midpoint Rule. Midpoints of drawn rectangles are used where . Trapezoidal Rule.

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