Explanation Given: Function f ( t ) = 6 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 ) = 6 t Also, the interval is 0 ≤ t ≤ 5 Area under the graph is calculated as ∫ 0 5 ( 6 t ) d t 6 ∫ 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 6 ∫ 0 5 ( t ) d t = 6 [

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.3, Problem 21P

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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.

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Chapter 6.3, Problem 20P

Chapter 6.3, Problem 22P

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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.

Solution Summary: The author calculates the area under the graph of f(t)=6t 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.

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Chapter 6 Solutions