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5.2 Definite Integrals

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Quick Review

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Quick Review Solutions

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What you’ll learn about Riemann Sums The Definite Integral Computing Definite Integrals on a Calculator Integrability Essential Questions What is a definite integral and how do we find it on a calculator?

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Sigma Notation The Definite Integral as a Limit of Riemann Sums

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The Existence of Definite Integrals The Definite Integral of a Continuous Function on [a,b] The Definite Integral

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Example Using the Notation 1.The interval [-2, 4] is partitioned into n subintervals of equal length x = 6/ n. Let m k denote the midpoint of the k th subinterval. Express the limit as an integral.

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Area Under a Curve (as a Definite Integral) 2.Use the graph of the integrand and areas to evaluate the integral.

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Area Under a Curve (as a Definite Integral) 2.Use the graph of the integrand and areas to evaluate the integral.

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The Integral of a Constant 3.Evaluate the integral

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Example Using NINT 4.Evaluate numerically.

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Pg. 251, 5.2 #1-35 odd

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