Explanation Given information: The table gives the slope f ' ( x k ) for points x k located at 0.3 unit intervals on a certain curve defined by y = f ( x ) . x k f ' ( x k ) 0.0 3.7 0.3 3.9 0.6 4.1 0.9 4.1 1.2 4.2 1.5 4.4 1.8 4.6 2.1 4.9 2.4 5.2 2.7 5.5 3.0 6.0 Formula used: Let f be continuous on [ a , b ] . The trapezoidal rule for approximating ∫ a b f ( x ) d x is given by b − a 2 n [ f ( a ) + 2 f ( x 1 ) + 2 f ( x 2 ) + ... + 2 f ( x n − 1 ) + f ( b ) ] Calculation: If f ' is continuous on the interval [ a , b ] , then the surface generated by revolving about y-axis the arc of the curve y = f ( x ) on [ a , b ] has surface area s = 2 π ∫ a b x 1 + [ f ' ( x ) ] 2 d x Let g ( x ) = x 1 + [ f ' ( x ) ] 2 , [ a , b ] = [ 0.0 , 3.0 ] and n = 10. The trapezoidal rule for approximating ∫ a b g ( x ) d x is given by b − a 2 n [ g ( a ) + 2 g ( x 1 ) + 2 g ( x 2 ) +

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Question

Chapter 6.4, Problem 52PS

To determine

To estimate:The surface area generated when y=f(x) is revolved about y-axis over the interval [0,3] using trapezoidal rule.

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Chapter 6.4, Problem 51PS

Chapter 6.4, Problem 53PS

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Find the largest rectangle (that is, the rectangle with largest area)that fits inside the graph of the parabola y = x2 below the line y = a (a is an unspecifiedconstant value), with the top side of the rectangle on the horizontal line y = a

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Chapter 6 Solutions

Student's Solution and Survival Manual for Calculus

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To estimate: The surface area generated when y = f ( x ) is revolved about y-axis over the interval [ 0 , 3 ] using trapezoidal rule.

Solution Summary: The author calculates the surface area generated by y=f(x) is 45.2335 square units.

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To estimate:The surface area generated when y=f(x) is revolved about y-axis over the interval [0,3] using trapezoidal rule.

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Chapter 6 Solutions