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nn - 1(x) dx n + 1(x) dx wing. of the following is correct for odd powers of sine. 5....n · 2n 2n ..• (2n + 1)

nn - 1(x) dx n + 1(x) dx wing. of the following is correct for odd powers of sine. 5....n · 2n 2n ..• (2n + 1)

Calculus: Early Transcendentals
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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(a) Ose tne TeductIOT TOIara sin" (x) dx cos(x) sin" - 1(x) + n - 1 sin" - 2(x) dx, where n 2 2 is an integer to determine which of the following reduction formulas is correct. x/2 x/2 sin"(x) dx = n - 1 sin" - 2(x) dx Jo a/2 sin"(x) dx = n + 1 sin" + 2(x) dx /2 x/2 n - 2 sin"(x) dx = sin" - 1(x) dx in 1/2 x/2 n + 2 sin"(x) dx = sin" + 1(x) dx Jo (b) Use part (a) to evaluate the following. 1/2 | sin3(x) dx = 2/2 | sin (x) dx = (c) Use part (a) to determine which of the following is correct for odd powers of sine. x/2 1(x) dx = 1:3:5. ...n 2:4. 6. . .· 2n sin2n + 1, x/2 2. 4. 6 .... 2n sin2n + 1(x) dx = 3:5. 7 (2n + 1) .... 2. 4. 6·• .· 2n sin2n + 1(x) dx 1:3. 5 ....n 2/2 sin2n + 1(x) dx = 3:5:7.• .. (2n + 1) 2. 4. 6.• . · 2n
Transcribed Image Text:(a) Ose tne TeductIOT TOIara sin" (x) dx cos(x) sin" - 1(x) + n - 1 sin" - 2(x) dx, where n 2 2 is an integer to determine which of the following reduction formulas is correct. x/2 x/2 sin"(x) dx = n - 1 sin" - 2(x) dx Jo a/2 sin"(x) dx = n + 1 sin" + 2(x) dx /2 x/2 n - 2 sin"(x) dx = sin" - 1(x) dx in 1/2 x/2 n + 2 sin"(x) dx = sin" + 1(x) dx Jo (b) Use part (a) to evaluate the following. 1/2 | sin3(x) dx = 2/2 | sin (x) dx = (c) Use part (a) to determine which of the following is correct for odd powers of sine. x/2 1(x) dx = 1:3:5. ...n 2:4. 6. . .· 2n sin2n + 1, x/2 2. 4. 6 .... 2n sin2n + 1(x) dx = 3:5. 7 (2n + 1) .... 2. 4. 6·• .· 2n sin2n + 1(x) dx 1:3. 5 ....n 2/2 sin2n + 1(x) dx = 3:5:7.• .. (2n + 1) 2. 4. 6.• . · 2n
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