3. Consider the integral / sin x dx. (a) Evaluate the integral by an appropriate reduction formula in Section 8.1, and write the constant added at the end as C1. (b) Evaluate the integral by the method of Section 8.2 (i.e., by factoring out sin x and by writing the rest of the integrand in terms of cos x), and write the constant added at the end as C2. (c) Show that the results found in (a) and (b) are compatible, by finding a relationship between C1 and C2. (Hint: Eliminate sinx from the answers in (a) and/or (b).)
3. Consider the integral / sin x dx. (a) Evaluate the integral by an appropriate reduction formula in Section 8.1, and write the constant added at the end as C1. (b) Evaluate the integral by the method of Section 8.2 (i.e., by factoring out sin x and by writing the rest of the integrand in terms of cos x), and write the constant added at the end as C2. (c) Show that the results found in (a) and (b) are compatible, by finding a relationship between C1 and C2. (Hint: Eliminate sinx from the answers in (a) and/or (b).)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 34E
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Question
Transcribed Image Text:3. Consider the integral / sin
sin x dx.
(a) Evaluate the integral by an appropriate reduction formula in Section 8.1, and write the constant
added at the end as C1.
(b) Evaluate the integral by the method of Section 8.2 (i.e., by factoring out sin x and by writing
the rest of the integrand in terms of cos x), and write the constant added at the end as C2.
(c) Show that the results found in (a) and (b) are compatible, by finding a relationship between C1
and C2. (Hint: Eliminate sin x from the answers in (a) and/or (b).)
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