Explanation Second Fundamental Theorem of Calculus: Let f ( x ) be continuous on an interval I , let a ∈ I and for x ∈ I , define F ( x ) = ∫ a x f ( t ) d t for all x ∈ I Then F ( x ) is differentiable on I and F ' ( x ) = f ( x ) for all x ∈ I In other words, if f is continuous on an interval I , let a ∈ I and for x ∈ I , then d d x ( ∫ a x f ( t ) d t ) = f ( x ) Chain Rule: If f is continuous on an open interval I containing the values of differentiable functions y = a ( x ) & y = b ( x ) , then d d x [ ∫ a ( x ) b ( x ) f ( t ) d t ] = f ( b ( x ) ) b ' ( x ) − f ( a ( x ) ) a ' ( x ) Given: A ( x ) = ∫ 2 x cos t 1 + t d t Formula used: Second Fundamental Theorem of Calculus: Let f ( x ) be continuous on an interval I , let a ∈ I and for x ∈ I , define F ( x ) = ∫ a x f ( t ) d t for all x ∈ I Then F

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ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 5, Problem 89CRE

To determine

To Determine:

The value of $A' (π)$ , where $A (x) = \int_{2}^{x} \frac{\cos t}{1 + t} d t$ .

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Chapter 5, Problem 88CRE

Chapter 5, Problem 90CRE

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Chapter 5 Solutions

EBK CALCULUS

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The value of A ' ( π ) , where A ( x ) = ∫ 2 x cos t 1 + t d t .

Solution Summary: The author explains the Second Fundamental Theorem of Calculus: Let f ( x ) be continuous on an interval I, let a I and for y.

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To Determine:

The value of $A' (π)$ , where $A (x) = \int_{2}^{x} \frac{\cos t}{1 + t} d t$ .

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Chapter 5 Solutions

The value of A ' ( π ) , where A ( x ) = ∫ 2 x cos t 1 + t d t .

Solution Summary: The author explains the Second Fundamental Theorem of Calculus: Let f ( x ) be continuous on an interval I, let a I and for y.

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To Determine: The value of A'(π), where A(x)=∫2xcost1+tdt.

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Chapter 5 Solutions

To Determine:

The value of $A' (π)$ , where $A (x) = \int_{2}^{x} \frac{\cos t}{1 + t} d t$ .