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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F671be518-f9e6-4df9-9304-33791fefeccb%2F774c3e89-e727-44c2-ba14-25d1220655ac%2Fgddg58s_processed.png&w=3840&q=75)
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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