Explanation Let the interval [ a , b ] be divided into n subintervals each of width h by the points a = x 0 , x 1 ,…, x n = b . Then think of each of the subintervals as n slices of equal thickness h which is very close to being a right circular cylinder. The volume of the right circular cylinder is π r 2 h . Here, in this case the height of each slice is h as shown in Figure ( 1 ) . The radius of the circular base of each slice is f ( x i ) . Figure ( 1 ) Hence, the volume is approximated by π [ f ( x i ) ] 2 h . The volume will be approximated by the sum of volumes of the slices, V ≈ ∑ i = 1 n π [ f ( x i ) ] 2 h

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Chapter 8.CR, Problem 9CR

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If the volume of the solid formed by revolving the function f about the x-axis on [−4,5] is given by ∫−45π(x+4)2dx is true or false.

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Chapter 8.CR, Problem 8CR

Chapter 8.CR, Problem 10CR

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Ch. 8.1 - YOUR TURN Use the trapezoidal rule with n=4 to...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

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To state: If the volume of the solid formed by revolving the function f about the x -axis on [ − 4 , 5 ] is given by ∫ − 4 5 π ( x + 4 ) 2 d x is true or false.

Solution Summary: The author states that if the volume of the solid formed by revolving the function f about the x-axis is true or false, it will be approximated by the sum of

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To state:

If the volume of the solid formed by revolving the function f about the x-axis on [−4,5] is given by ∫−45π(x+4)2dx is true or false.

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Chapter 8 Solutions

To state: If the volume of the solid formed by revolving the function f about the x -axis on [ − 4 , 5 ] is given by ∫ − 4 5 π ( x + 4 ) 2 d x is true or false.

Solution Summary: The author states that if the volume of the solid formed by revolving the function f about the x-axis is true or false, it will be approximated by the sum of

Concept explainers

Videos

To state: If the volume of the solid formed by revolving the function f about the x-axis on [−4,5] is given by ∫−45π(x+4)2dx is true or false.

Want to see the full answer?

Chapter 8 Solutions

To state:

If the volume of the solid formed by revolving the function f about the x-axis on [−4,5] is given by ∫−45π(x+4)2dx is true or false.