Evaluate Definite Integrals

 

The Fundamental Theorem of Calculus

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Fundamental Theorem of Calculus is presented and justified.

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Statement and explanation of the two forms for the Fundamental Theorem of Calculus.

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Using the Fundamental Theorem to evaluate an integral.

Six questions which involve finding areas under curves and evaluating definite integrals.

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Algorithm for Computing Riemann Integrals

General algorithm for evaluating integrals using the Fundamental Theorem of Calculus.

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The Two Fundamental Theorems of Calculus

Statement and explanation of the First and Second Fundamental Theorems, with examples.

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Proof of the Two Fundamental Theorems

An intuitive argument justifying the Second Fundamental Theorem and a complete proof of the First Fundamental Theorem, including remarks about these theorems as they relate to definite and indefinite integrals.

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Functions Defined By Integrals

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Three part question finding bounds on the values of a function defined in terms of an integral and finding where the function is concave up or concave down.

Four part question which involves finding the derivative, critical points, and an estimation of a function which is defined in terms of an integral.

Four part question which involves finding critical points and values of a function which is defined in terms of an integral.

Finding the first and second derivatives of a function defined in terms of an integral, and expressing another integral in terms of that function.

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