Explanation Given: The function is f ( x ) = x bounded by y = 0 , x = 1 , x = 4 . Approach: If f ( x ) is nonnegative and R is the region between f ( x ) and the x -axis from x = a to x = b , the volume of the solid formed by rotating R about the x -axis is given by, V = ∫ a b π [ f ( x ) ] 2 d x Calculation: The graph of the function f ( x ) = x bounded by the curves is shown in Figure ( 1 ) . Figure ( 1 ) Volume of the solid of revolution is calculated as, V = ∫ a b π [ f ( x ) ] 2 d x ... ( 1 ) Here, x = a and x = b are x -intercepts . Substitute 1 for a , 4 for b and x for f ( x ) in equation ( 1 )

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Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 8.3, Problem 7E

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To find:

The volume of the solid of revolution bounded by the region f(x)=x about x- axis.

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Chapter 8.3, Problem 6E

Chapter 8.3, Problem 8E

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EBK CALCULUS FOR THE LIFE SCIENCES

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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The volume of the solid of revolution bounded by the region f ( x ) = x about x - axis.

Solution Summary: The author calculates the volume of the solid formed by rotating R about the x-axis.

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To find:

The volume of the solid of revolution bounded by the region f(x)=x about x- axis.

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Chapter 8 Solutions

The volume of the solid of revolution bounded by the region f ( x ) = x about x - axis.

Solution Summary: The author calculates the volume of the solid formed by rotating R about the x-axis.

Concept explainers

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To find: The volume of the solid of revolution bounded by the region f(x)=x about x- axis.

Want to see the full answer?

Chapter 8 Solutions

To find:

The volume of the solid of revolution bounded by the region f(x)=x about x- axis.