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(a) Use the reduction formula "(x) dx cos(x) sin" - '(x) + 1/ sin" - 2(x) dx, where n 2 2 is an integer to determine which of the following reduction formulas is correct. /2 /2 n+1 sin"(x) dx = sin + 2(x) dx Jo m/2 'm/2 sin"(x) dx n- 2 | sin" - (x) dx m/2 /2 sin"(x) dx n+ 2 I sin" + (x) dx m/2 7/2 % sin"(x) dx =0 - 1 sin - 2(x) dx (b) Use part (a) to evaluate the following. /2 I sin (x) dx = '피2 sin (x) dx = ( (c) Use part (a) to determine which of the following is correct for odd powers of sine. '피2 I sin?n + 1(x) dx = 2.4.6...· 2n (2n + 1) 3.5:7.... m/2 (2n + 1) 3.5.7.... I sin?n + 1(x) dx = 2.4.6...· 2n /2 2.4.6. .· 2n I sin2n + 1(x) dx = 1:3. 5...n /2 1:3.5.. .n sin?n + 1(x) dx = 2.4. 6...· 2n

(a) Use the reduction formula "(x) dx cos(x) sin" - '(x) + 1/ sin" - 2(x) dx, where n 2 2 is an integer to determine which of the following reduction formulas is correct. /2 /2 n+1 sin"(x) dx = sin + 2(x) dx Jo m/2 'm/2 sin"(x) dx n- 2 | sin" - (x) dx m/2 /2 sin"(x) dx n+ 2 I sin" + (x) dx m/2 7/2 % sin"(x) dx =0 - 1 sin - 2(x) dx (b) Use part (a) to evaluate the following. /2 I sin (x) dx = '피2 sin (x) dx = ( (c) Use part (a) to determine which of the following is correct for odd powers of sine. '피2 I sin?n + 1(x) dx = 2.4.6...· 2n (2n + 1) 3.5:7.... m/2 (2n + 1) 3.5.7.... I sin?n + 1(x) dx = 2.4.6...· 2n /2 2.4.6. .· 2n I sin2n + 1(x) dx = 1:3. 5...n /2 1:3.5.. .n sin?n + 1(x) dx = 2.4. 6...· 2n

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) Use the reduction formula sin") de = - cos(o) sin" - "6) + -1 / sin" -2(x) dx, where n 22 is an integer sin"(x) dx to determine which of the following reduction formulas is correct. '피2 sin"(x) dx = '피2 sin" + 2(x) dx n+1 '피2 sin" - (x) dx /2 sin"(x) dx = n- 2 /2 sin" + (x) dx /2 n+ 2 sin"(x) dx 7/2 sin" - 2(x) dx of /2 n- 1 sin"(x) dx = (b) Use part (a) to evaluate the following. /2 sin (x) dx = sin (x) dx = '피2 (c) Use part (a) to determine which of the following is correct for odd powers of sine. '피2 sin?n + 1(x) dx 2.4.6..·· 2n - (2n + 1) (2n + 1) 2.4.6. .·· 2n 3.5:7... /2 sin2n + 1(x) dx 3.5.7.... = /2 sin?n + 1(x) dx = 2.4. 6...· 2n 1:3.5. ..n /2 1:3.5. ·..n sin?n + 1(x) dx 2.4. 6. ..· 2n
Transcribed Image Text:(a) Use the reduction formula sin") de = - cos(o) sin" - "6) + -1 / sin" -2(x) dx, where n 22 is an integer sin"(x) dx to determine which of the following reduction formulas is correct. '피2 sin"(x) dx = '피2 sin" + 2(x) dx n+1 '피2 sin" - (x) dx /2 sin"(x) dx = n- 2 /2 sin" + (x) dx /2 n+ 2 sin"(x) dx 7/2 sin" - 2(x) dx of /2 n- 1 sin"(x) dx = (b) Use part (a) to evaluate the following. /2 sin (x) dx = sin (x) dx = '피2 (c) Use part (a) to determine which of the following is correct for odd powers of sine. '피2 sin?n + 1(x) dx 2.4.6..·· 2n - (2n + 1) (2n + 1) 2.4.6. .·· 2n 3.5:7... /2 sin2n + 1(x) dx 3.5.7.... = /2 sin?n + 1(x) dx = 2.4. 6...· 2n 1:3.5. ..n /2 1:3.5. ·..n sin?n + 1(x) dx 2.4. 6. ..· 2n
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