Is it possible to use the reduction formula for cosine on this integral? ∫[(1 - cos^(2)Θ) * cosΘ] dx Futhermore, is it also possible to convert the answer into terms of x by using trig identities/subtitutions (via the right triangle)? The original equation for the textbook is ∫sqrt(x^2 - 1)/x^4 dx . I was able to use trigonometic substitution to get to ∫[(1 - cos^(2)Θ) * cosΘ] dx, but I did not get the correct answer when I tried to use the reduction formula for cosine. My textbook says the answer is (1/3)*((x^2 - 1)^(3/2))/x^3 + C . The question is from Stewart Calculus, Chapter 7 Section 3, #5.
Is it possible to use the reduction formula for cosine on this integral? ∫[(1 - cos^(2)Θ) * cosΘ] dx Futhermore, is it also possible to convert the answer into terms of x by using trig identities/subtitutions (via the right triangle)? The original equation for the textbook is ∫sqrt(x^2 - 1)/x^4 dx . I was able to use trigonometic substitution to get to ∫[(1 - cos^(2)Θ) * cosΘ] dx, but I did not get the correct answer when I tried to use the reduction formula for cosine. My textbook says the answer is (1/3)*((x^2 - 1)^(3/2))/x^3 + C . The question is from Stewart Calculus, Chapter 7 Section 3, #5.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Is it possible to use the reduction formula for cosine on this
∫[(1 - cos^(2)Θ) * cosΘ] dx
Futhermore, is it also possible to convert the answer into terms of x by using trig identities/subtitutions (via the right triangle)?
The original equation for the textbook is ∫sqrt(x^2 - 1)/x^4 dx .
I was able to use trigonometic substitution to get to ∫[(1 - cos^(2)Θ) * cosΘ] dx, but I did not get the correct answer when I tried to use the reduction formula for cosine.
My textbook says the answer is (1/3)*((x^2 - 1)^(3/2))/x^3 + C .
The question is from Stewart Calculus, Chapter 7 Section 3, #5.
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