Explanation Given: The derivative f ' ( x ) = e − x 2 , f ( 1 ) = 0 Concept Used: Second Fundamental Theorem of Calculus stats that if f is continuous on [ a , b ] and we define F ( x ) = ∫ a x f ( t ) d t for all x ∈ [ a , b ] , then F is continuous on [ a , b ] and differentiable on ( a , b ) . Fis antiderivative of f , that is, F ' ( x ) = f ( x ) . If f is continuous on [ a , b ] and u ( x ) is differentiable on [ a , b ] , then for all x ∈ [ a , b ] , d d x ∫ a u ( x ) f

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4.7, Problem 53S

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The function f that has the derivative f'(x)=e−x2 and satisfy the value f(1)=0 .

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Chapter 4.7, Problem 52S

Chapter 4.7, Problem 54S

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Chapter 4 Solutions

Calculus

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The function f that has the derivative f ' ( x ) = e − x 2 and satisfy the value f ( 1 ) = 0 .

Solution Summary: The author states that if f is continuous on left[a,bright], then he is antiderivative.

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The function f that has the derivative f'(x)=e−x2 and satisfy the value f(1)=0 .

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