A sine reduction formula Use integration by parts to obtain a reduction formula for positive integers n: sin" x dx = -sin-1 xcos x + (n – 1) / sin* -2 x cos? x dx. Then use an identity to obtain the reduction formula |sin" x dx = sin"-x cos x + -/sin"-2x dx. Use this reduction formula to evaluate S sinº x dx.

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...
icon
Related questions
Question
A sine reduction formula Use integration by parts to obtain a
reduction formula for positive integers n:
sin" x dx = -sin-1 xcos x + (n – 1) / sin*
-2 x cos? x dx.
Then use an identity to obtain the reduction formula
|sin" x dx =
sin"-x cos x
+
-/sin"-2x dx.
Use this reduction formula to evaluate S sinº x dx.
Transcribed Image Text:A sine reduction formula Use integration by parts to obtain a reduction formula for positive integers n: sin" x dx = -sin-1 xcos x + (n – 1) / sin* -2 x cos? x dx. Then use an identity to obtain the reduction formula |sin" x dx = sin"-x cos x + -/sin"-2x dx. Use this reduction formula to evaluate S sinº x dx.
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning