Explanation Given information: The function, y = tan x Concept used: For any nonnegative and continuous function y = f ( x ) on the closed interval [ a , b ] , the volume of the solid generated by rotating about the x -axis using the disk method is given by the definite integral, ∫ a b π y 2 d x tan 2 x = sec 2 x − 1 Calculation: We know that the volume of the solid generated by rotating the curve y = f ( x ) from x = a to x = b about the x -axis using the disk method is given by the definite integral, ∫ a b π y 2 d x . So using this concept the volume of the solid obtained by revolving y = tan x for 0 ≤ x ≤ π 6 , about x -axis is given by the definite integral V = ∫ 0 π 6 π ( tan x ) 2 d x = π ∫ 0 π 6 tan 2 x d x Now first we will compute the indefinite integral by substitution method

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 7.2, Problem 66E

To determine

To compute the volume of the solid obtained by revolving y=tanx for 0≤x≤π6, about x -axis

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Chapter 7.2, Problem 65E

Chapter 7.2, Problem 67E

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Chapter 7 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

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To compute the volume of the solid obtained by revolving y = tan x for 0 ≤ x ≤ π 6 , about x -axis

Solution Summary: The author explains that the volume of the solid obtained by revolving y=mathrmtanx is given by the definite integral.

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To compute the volume of the solid obtained by revolving y=tanx for 0≤x≤π6, about x -axis

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