In this problem, let fƒ(r) = ln| sec x|. (a) Graph y = f(x). Write down a definite integral that computes the arclength of the graph of f(x) from x = 0 to r = R/4. Be sure to carefully explain how you took the derivative of f(x). (b) Compute the definite integral in part (a). Be sure to mention any trig identities you use and to discuss the sign of the integrand. You will need to know that f sec rdr = In | sec x + tan x| +C.
In this problem, let fƒ(r) = ln| sec x|. (a) Graph y = f(x). Write down a definite integral that computes the arclength of the graph of f(x) from x = 0 to r = R/4. Be sure to carefully explain how you took the derivative of f(x). (b) Compute the definite integral in part (a). Be sure to mention any trig identities you use and to discuss the sign of the integrand. You will need to know that f sec rdr = In | sec x + tan x| +C.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Step 1
Part(a)
The given function is,
Now, differentiate the given function with respect to x up to first order.
Step 2
So, the arclength of the given function from 0 to is given by the formula,
Substitute for into the formula .
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