Explanation Given Information: The velocity of cat Price Sadar in t seconds after he began is v ( t ) = − π 2 sin [ π 4 ( t − 2 ) ] ft/sec if cat Price Sadar is pacing back and forth along his favorite window ledge. Formula Used: The total change of the function from x = a to x = b is, ∫ a b f ( x ) d x . Where, function f ( x ) is the rate of change of quantity. The formula for the integration of the function is given by ∫ sin ( a x + b ) d x = − 1 a x + b cos ( a x + b ) + C , where the function is f ( x ) = sin ( a x + b ) , and a and b are constants, with a ≠ 0 . Constant multiple rule is ∫ k ⋅ g ( x ) d x = k ∫ g ( x ) d x where k is a constant. Calculation: Consider the provided function v ( t ) = − π 2 sin [ π 4 ( t − 2 ) ] ft/sec . Determine the total change in position from 0 to 10 seconds using definite integral, v ( t ) = ∫ 0 10 ( − π 2 sin [ π 4 ( t − 2 ) ] ) d t Now, evaluate the integral of the function by applying constant multiple rules and using shortcut formula of ∫ cos ( a x ) d x = 1 a sin ( a x ) + C to determine the distance, ∫ 0 10

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

7th Edition

ISBN: 9781337291293

Author: Waner, Stefan; Costenoble, Steven

Publisher: Brooks Cole

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Chapter 9.3, Problem 62E

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Chapter 9.3, Problem 61E

Chapter 9.3, Problem 63E

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Chapter 9 Solutions

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

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The distance covered by the cat Prince Sadar after 10 seconds to pace.

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Chapter 9 Solutions