Explanation Given: Function f ( t ) = − 2 t and the interval is 0 ≤ t ≤ 5 . Formula Used: As per the fundamental theorem of calculus, if f is continuous on the interval [ a , b ] and F ( x ) is antiderivative of f , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) Calculation: Function is given as f ( t ) = − 2 t Also, the interval is 0 ≤ t ≤ 5 . Area under the graph is calculated as ∫ 0 5 ( − 2 t ) d t − 2 ∫ 0 5 ( t ) d t (Using the identity ∫ a . f ( x ) d x = a ∫ f ( x ) d x ) Using the fundamental theorem of calculus, we get − 2 ∫ 0 5 ( t ) d

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 6.3, Problem 24P

To determine

To find the area under the graph of f(t) for 0≤t≤5 using the Fundamental Theorem of Calculus. Also, compare the answer with the answer you get using area of triangles.

f(t)=−2t

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Chapter 6.3, Problem 23P

Chapter 6.3, Problem 25P

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Chapter 6 Solutions

APPLIED CALCULUS (WILEY PLUS)

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To find the area under the graph of f ( t ) for 0 ≤ t ≤ 5 using the Fundamental Theorem of Calculus. Also, compare the answer with the answer you get using area of triangles. f ( t ) = − 2 t

Solution Summary: The author calculates the area under the graph of f(t) using the Fundamental Theorem of Calculus.

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To find the area under the graph of f(t) for 0≤t≤5 using the Fundamental Theorem of Calculus. Also, compare the answer with the answer you get using area of triangles.

f(t)=−2t

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Chapter 6 Solutions

To find the area under the graph of f ( t ) for 0 ≤ t ≤ 5 using the Fundamental Theorem of Calculus. Also, compare the answer with the answer you get using area of triangles. f ( t ) = − 2 t

Solution Summary: The author calculates the area under the graph of f(t) using the Fundamental Theorem of Calculus.

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To find the area under the graph of f(t) for 0≤t≤5 using the Fundamental Theorem of Calculus. Also, compare the answer with the answer you get using area of triangles. f(t)=−2t

Want to see the full answer?

Chapter 6 Solutions

To find the area under the graph of f(t) for 0≤t≤5 using the Fundamental Theorem of Calculus. Also, compare the answer with the answer you get using area of triangles.

f(t)=−2t