'Trapezoidal rule' diaporamas de présentation

TECHNIQUES OF INTEGRATION

7. TECHNIQUES OF INTEGRATION. TECHNIQUES OF INTEGRATION. There are two situations in which it is impossible to find the exact value of a definite integral. . TECHNIQUES OF INTEGRATION.

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Numerical Methods

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Numerical Differentiation and Integration

Numerical Differentiation and Integration. Standing in the heart of calculus are the mathematical concepts of differentiation and integration :. Figure PT6.1. Figure PT6.2. Noncomputer Methods for Differentiation and Integration.

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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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Geology and Surveying 70380 (Part B - Surveying) Volumes and DTMs

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Integration

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Romberg Rule of Integration

Romberg Rule of Integration. Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates. Romberg Rule of Integration http://numericalmethods.eng.usf.edu. f(x). y. a. b. x.

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Integration

Integration Topic: Romberg Rule Major: Computer Engineering f(x) y a b x Basis of Romberg Rule Integration The process of measuring the area under a curve. Where: f(x) is the integrand a= lower limit of integration b= upper limit of integration What is The Romberg Rule?

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Area calculation

Area calculation. Area is divided into triangles, rectangles, squares or trapeziums Area of the one figure (e.g. triangles, rectangles, squares or trapeziums) is calculated and multiplied by total number of figures. Area along the boundaries is calculated as

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01052006 ??????????????????? (Engineering Computation) Numerical Integration Formulas

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Techniques of Integration

Techniques of Integration. Substitution Rule Integration by Parts Trigonometric Integrals Trigonometric Substitution Integration of Rational Functions by Partial Fractions Rationalizing Substitutions The Continuous Functions Which Do not Have Elementary Anti-derivatives. Improper Integrals

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NUMERICAL INTEGRATION

NUMERICAL INTEGRATION. Motivation: Most such integrals cannot be evaluated explicitly. Many others it is often faster to integrate them numerically rather than evaluating them exactly using a complicated antiderivative of f(x) Example:

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Finding the area of curved irregular shapes

Finding the area of curved irregular shapes. LEAVING CERTIFCATE ORDINARY & HIGHER LEVELS. Find the area of your shape. Work as accurately as you can in centimetres!. 1 A. You found the area of an A4 page!. 1 B. 1 A. Trapezoidal Rule. (a) Find the area of the stained glass window.

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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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Numerical Integration

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Trapezoidal Rule

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Chapter 21 section 5 1 ? 3 Rule The Multiple-Application S impsons

Chapter 21 section 5 1 ? 3 Rule The Multiple-Application S impsons. the rule can be improved by dividing the integration interval into a number of segments : n h=(b-a) ? h : width n : number of segments.

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7.7 Approximate Integration

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