Explanation Proof: Since, G is the anti derivative of f . ∫ a b f ( x ) d x = [ G ( x ) ] a b = G ( b ) − G ( a ) Therefore, A ( x ) = ∫ 0 x f ( t ) <

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ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Question

Chapter 4.7, Problem 63P

To determine

To prove: that if f has an ant derivative, then the function A(x)=∫0xf(t)dt must also be an anti derivative of f .

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Chapter 4.7, Problem 62A

Chapter 4.7, Problem 64P

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Chapter 4 Solutions

Calculus

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To prove: that if f has an ant derivative, then the function A ( x ) = ∫ 0 x f ( t ) d t must also be an anti derivative of f .

Solution Summary: The author proves that if f has an ant derivative, then the function A(x)=displaystyle int

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To prove: that if f has an ant derivative, then the function A(x)=∫0xf(t)dt must also be an anti derivative of f .

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Chapter 4 Solutions