Explanation Given: Function f ( t ) = 10 − 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 ) = 10 − 2 t Also, the interval is 0 ≤ t ≤ 5 . Area under the graph is calculated as ∫ 0 5 ( 10 − 2 t ) d t Use the Sum Rule ∫ f ( x ) ± g ( x ) d x = ∫ f ( x ) d x ± ∫ g ( x ) d x . ∫ 0 5 ( 10 − 2 t ) d t = ∫ 0 5 ( 10 ) d t − ∫ 0 5 ( 2 t ) d t Use the identity ∫ a . f ( x ) d x = a ∫ f ( x ) d x

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 6.3, Problem 22P

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)=10−2t

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Chapter 6.3, Problem 21P

Chapter 6.3, Problem 23P

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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 ) = 10 − 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)=10−2t

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 ) = 10 − 2 t

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

Concept explainers

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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)=10−2t

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)=10−2t