Explanation Given: The derivative d d x ∫ 1 x ln t d t . 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 (

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 4.7, Problem 42S

To determine

The derivative ddx∫1xlnt dt using the Second Fundamental Theorem of Calculus.

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Chapter 4.7, Problem 41S

Chapter 4.7, Problem 43S

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Chapter 4 Solutions

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The derivative d d x ∫ 1 x ln t d t using the Second Fundamental Theorem of Calculus.

Solution Summary: The author explains the second fundamental theorem of calculus, which states that if f is continuous on left[a,bright], then it is antiderivative of

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The derivative ddx∫1xlnt dt using the Second Fundamental Theorem of Calculus.

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Chapter 4 Solutions