Explanation Given : Function y = tan x and interval [ 0 , π 4 ] as well as revolution of this function about x axis. There is a prebuilt formula to calculate the total surface area of revolution when the graph of a function, in a given interval is rotated along x axis and for that we need the differentiation of this function with respect to x also, so that its value can be put in said formula, to get the required surface area. Formula to be used : Required surface area A is calculated using the formula, A = ∫ a b 2 π y d s Where d s is calculated using the formula, d s = 1 + ( d y d x ) 2 d x And ‘ a ’ be the lower limit of the given interval and ‘ b ’ be the upper limit of that interval. Calculation : Here for the given function y = tan x , its first derivation with respect to x is : d y d x = d d x tan x = sec 2 x Thus, d s = 1 + ( sec 2 x ) 2 d x

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ISBN: 9781319411657

Author: Rogawski

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Question

Chapter 8.2, Problem 50E

To determine

The surface area of revolution about x axis of the function $y = \tan x$ over the interval $[0, \frac{π}{4}]$ .

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Chapter 8.2, Problem 49E

Chapter 8.2, Problem 51E

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Chapter 8 Solutions

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Knowledge Booster

The surface area of revolution about x axis of the function y = tan x over the interval [ 0 , π 4 ] .

The surface area of revolution about x axis of the function y=tanx over the interval [0,π4].

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Chapter 8 Solutions

The surface area of revolution about x axis of the function $y = \tan x$ over the interval $[0, \frac{π}{4}]$ .