Explanation Given Information: The velocity of dog Miranda t seconds after she began is v ( t ) = 3 π cos [ π 2 ( t − 1 ) ] ft/sec if she is running back and forth along a 12 -foot stretch of garden. 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 ∫ cos ( a x + b ) d x = 1 a x + b sin ( a x + b ) + C , where the function is f ( x ) = cos ( 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 ) = 3 π cos [ π 2 ( t − 1 ) ] ft/sec . Determine the total change in position from 0 to 10 seconds using definite integral, v ( t ) = ∫ 0 10 3 π cos [ π 2 ( t − 1 ) ] 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 position

7th Edition

ISBN: 9781337291408

Author: Stefan Waner, Steven Costenoble

Publisher: Brooks Cole

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 9.3, Problem 61E

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To calculate: The distance covered by the Miranda after 10 seconds, when she starting the run.

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Chapter 9.3, Problem 60E

Chapter 9.3, Problem 62E

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Chapter 9 Solutions

Applied Calculus, Loose-leaf Version

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The distance covered by the Miranda after 10 seconds, when she starting the run.

Solution Summary: The author calculates the distance covered by the Miranda after 10 seconds, when she starts the run.

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Chapter 9 Solutions