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d. Use your work in (a)-(c) to evaluate the indefinite integral f sin³(x) dx. e. Use a similar approach to evaluate ſcos³(x) dx.

d. Use your work in (a)-(c) to evaluate the indefinite integral f sin³(x) dx. e. Use a similar approach to evaluate ſcos³(x) dx.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Only need answers for d and e please, thank you!

It would be helpful if I could get hand-written explanations as they are easier to read in math than typed. Please and thank you! 9. Consider the indefinite integral f sin³(x) dx. a. Explain why the substitution u = sin(x) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin²(x) + cos²(x) = 1. By observing that sin³(x) = sin(x) · sin²(x), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(x) with another function. c. Explain why the substitution u = cos(x) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)-(c) to evaluate the indefinite integral sin³ (x) dx. e. Use a similar approach to evaluate cos³(x) dx.
Transcribed Image Text:It would be helpful if I could get hand-written explanations as they are easier to read in math than typed. Please and thank you! 9. Consider the indefinite integral f sin³(x) dx. a. Explain why the substitution u = sin(x) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin²(x) + cos²(x) = 1. By observing that sin³(x) = sin(x) · sin²(x), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(x) with another function. c. Explain why the substitution u = cos(x) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)-(c) to evaluate the indefinite integral sin³ (x) dx. e. Use a similar approach to evaluate cos³(x) dx.
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