Explanation Given Information: The volume V is given by V = ∫ 0 R v ( 2 π r ) d r , R = 0.30 cm and v = ( 0.30 − 3.33 r 2 ) cm / s . Formula used: To calculate a definite integral , evaluate the indefinite integral and then substitute the limits of the integral. The value of the integral ∫ x n d x = x n + 1 n + 1 . Calculation: Consider the volume V is given by V = ∫ 0 R v ( 2 π r ) d r , R = 0.30 cm and v = ( 0.30 − 3.33 r 2 ) cm / s . Evaluate the integral is V = ∫ 0 R v ( 2 π r ) d r . Since, v = ( 0.30 − 3.33 r 2 ) and R = 0.30 . Thus, the integral is V = ∫ 0 0.30 ( 0.30 − 3.33 r 2 ) ( 2 π r ) d r = ∫ 0 0.30 ( 0.6 π r − 6.66 π r 3 ) d r Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral. Thus, evaluate the integral. Simplify the integral by the use of the formula ∫ x n d x = x n + 1 n + 1 , ∫ 0 0

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Chapter 13.2, Problem 63E

To determine

To calculate: The volume of vessel if volume V is given by V=∫0Rv(2πr)dr, radius of the vessel R=0.30 cm and velocity of blood through vessel v=(0.30−3.33r2) cm/s and r is distance of the particular corpuscle from the center of the vessel.

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Chapter 13.2, Problem 62E

Chapter 13.2, Problem 64E

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Chapter 13 Solutions

MATHEMATICAL APPLICATIONS FOR THE MGT

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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The volume of vessel if volume V is given by V = ∫ 0 R v ( 2 π r ) d r , radius of the vessel R = 0.30 cm and velocity of blood through vessel v = ( 0.30 − 3.33 r 2 ) cm / s and r is distance of the particular corpuscle from the center of the vessel.

Solution Summary: The author evaluates the indefinite integral and substitutes its limits. The volume of the vessel is 0.04cm3.

To calculate: The volume of vessel if volume V is given by V=∫0Rv(2πr)dr, radius of the vessel R=0.30 cm and velocity of blood through vessel v=(0.30−3.33r2) cm/s and r is distance of the particular corpuscle from the center of the vessel.

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Chapter 13 Solutions