Explanation Given: The region is bounded by f ( x ) = tan ( x ) and the x axis on the interval [ 0 , π 2 ) . The region is revolved about the x axis and equation of x axis is y = 0 . Formula used: The volume of the solid (disk method) is ∫ a b π ( f 2 ( x ) − g 2 ( x ) ) d x ,where f ( x ) and g ( x ) is mentioned above. Definition used: Improper integral “If f is continuous on [ a , b ) , then ∫ a b f ( x ) d x = lim c → b − ∫ a c f ( x ) d x .” Theorem used: Fundamental theorem of calculus “If f is continuous on [ a , b ] and F is anti derivative of f , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) .” Calculation: Let y = g ( x ) , then g ( x ) = 0 . The region is bounded by f ( x ) = tan ( x ) and g ( x ) = 0 . The function f ( x ) = tan ( x ) is unbounded at the point x = π 2 on the interval [ 0 , π 2 ) . Let l = f 2 ( x ) − g 2 ( x ) . To find the volume of the solid, first find the value of l with f ( x ) = tan ( x ) and g ( x ) = 0 as follows, l = ( tan ( x ) ) 2 − 0 2 = tan 2 ( x ) Substitute the value of l = tan 2 ( x ) in the above mentioned volume of the solid formula and take a = 0 as lower limit and b = π 2 as upper limit

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

3rd Edition

ISBN: 9780134996103

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 8.9, Problem 73E

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To find: The volume of the solid or state it’s existence when the region R is revolved about the x axis.

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Chapter 8.9, Problem 72E

Chapter 8.9, Problem 74E

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Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

Ch. 8.1 - What change of variable would you use for the...Ch. 8.1 - Prob. 2QC Ch. 8.1 - Prob. 3QC Ch. 8.1 - Prob. 4QC Ch. 8.1 - What change of variables would you use for the...Ch. 8.1 - Prob. 2E Ch. 8.1 - What trigonometric identity is useful in...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E

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The volume of the solid or state it’s existence when the region R is revolved about the x axis.

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To find: The volume of the solid or state it’s existence when the region R is revolved about the x axis.

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Chapter 8 Solutions