Explanation Given Information: The area accumulation functions The second fundamental theorem of calculus Differentiating a composition involving an area accumulation function Properties of the natural logarithm function 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 integral ∫ a b f ( x ) d x is equal to the area accumulation function. If f is continuous on the interval [ a , b ] , where F ( x ) = ∫ a b f ( x ) d x , then F is continuous on [ a , b ] and differentiable on ( a , b ) .the function F is anti derivative of f ,that is , F ' ( x ) = f ( x ) .This is called the second fundamental theorem of calculus

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4.7, Problem 0C

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To Write: A summary of the material for topic “AREA ACCUMUALATION”.

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Chapter 4.7, Problem 3TB

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Calculus

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A summary of the material for topic “AREA ACCUMUALATION”.

Solution Summary: The author explains the second fundamental theorem of calculus, which differs a composition involving an area accumulation function.

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Chapter 4 Solutions