Explanation Given Information: The area accumulation functions The second fundamental theorem of calculus Considerthe area accumulation function ∫ a b f ( x ) d x If function f is continuous on the interval [a, b] The signed area between the graph of f and the x − axis is given by the definite ∫ a b f ( x ) d x Any definite integral or indefinite integral can be undone using it's differentiation function as explained below. Same way any differentiation can be undone using it's s integral as explained below. since the relationship between these is connected. If f is continuous on the interval [ a , b ] , where F ( x ) = ∫ a b f ( x ) d x continuous on $[a, b]$ and differentiable on ( a , b ) the function F is anti derivative of f , that is , F ′ ( x ) = f ( x )

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 4, Problem BCP

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To Explain: the integration as the opposite of differentiation

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Chapter 4, Problem ACP

Chapter 4, Problem CCP

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Chapter 4 Solutions

Loose-leaf Version for Calculus

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