Explanation Given information : y = x 2 and interval → [ 0 , 1 ] Formula used : Area of surface ( S ) = ∫ a b 2 π y 1 + ( d y d x ) 2 d x , a ≤ x ≤ b revolve about x − axis. ∫ x 2 − a 2 d x = x 2 x 2 − a 2 − a 2 2 ln | x + x 2 − a 2 | + C Calculation : Here, y = x 2 and 0 ≤ x ≤ 1 Differentiate function with respect to ‘ x’ , ⇒ d y d x = d d x ( x 2 ) ⇒ d y d x = 2 x Thus, area of surface generated about x − axis is Area of surface ( S ) = ∫ 0 1 2 π x 2 1 + ( 2 x ) 2 d x = 2 π ∫ 0 1 x 2 1 + 4 x 2 d x Let us assume, t = 1 + 4 x 2 ⇒ d t = 8 x d x When x → 0 , t → 1 and x → 1 , t → 5 Area of surface ( S ) = 2 π ∫ 1 5 x 2 t ⋅ d t 8 x = 2 π ∫ 1 5 x t ⋅ d t 8 = π 4 ∫ 1 5 t − 1 4 ⋅ t </

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 7.1, Problem 55PS

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To calculate : Area of surface generated by revolving the curve about the x − axis.

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Chapter 7.1, Problem 54PS

Chapter 7.1, Problem 56PS

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Chapter 7 Solutions

Calculus

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Area of surface generated by revolving the curve about the x − axis.

Solution Summary: The author calculates the area of surface generated by revolving the curve about the x axis.

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Chapter 7 Solutions