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4. Integrate: coss (30)sin² (30)do (State the strategy number you are using from the 6 strategies under "Powers of the T Functions" from our DL190FormulaSheet. This strategy must be stated correctly for any credit to be given.)

4. Integrate: coss (30)sin² (30)do (State the strategy number you are using from the 6 strategies under "Powers of the T Functions" from our DL190FormulaSheet. This strategy must be stated correctly for any credit to be given.)

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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Powers of the Trig Functions: 1) Integrals of the form: (sin" x cos" x dx m or n odd Strategy: If m is odd, save a sine factor and convert to cosine If n is odd, save a cosine factor and convert to sine 2) Integrals of the form: [sin"> Strategy: use angle identities: 1+ cos(2x) 2 2 cos² x = [sin" x cos" x dx m and n even and non-negative 2 -; sin′x= 1-cos(2x) 2 3) Integrals of the form: [sec" x tan" x dx ; if m is even Strategy: Save a sec² x and convert to tangent 4) Integrals of the form: [sec" x tan" x dx; if n is odd Strategy: Save a secx tanx and convert to secant 5) Stan" x dx n any positive integer Strategy: convert a tan² x to sec²x-1 and distribute; repeat if necessary 6) [sec" x dx ; mis odd Strategy: Integrate by parts *** If all else fails convert everything to sines and cosines
Transcribed Image Text:Powers of the Trig Functions: 1) Integrals of the form: (sin" x cos" x dx m or n odd Strategy: If m is odd, save a sine factor and convert to cosine If n is odd, save a cosine factor and convert to sine 2) Integrals of the form: [sin"> Strategy: use angle identities: 1+ cos(2x) 2 2 cos² x = [sin" x cos" x dx m and n even and non-negative 2 -; sin′x= 1-cos(2x) 2 3) Integrals of the form: [sec" x tan" x dx ; if m is even Strategy: Save a sec² x and convert to tangent 4) Integrals of the form: [sec" x tan" x dx; if n is odd Strategy: Save a secx tanx and convert to secant 5) Stan" x dx n any positive integer Strategy: convert a tan² x to sec²x-1 and distribute; repeat if necessary 6) [sec" x dx ; mis odd Strategy: Integrate by parts *** If all else fails convert everything to sines and cosines
4. Integrate: cos5 (30)sin² (30)do (State the strategy number you are using from the 6 strategies under "Powers of the Trig Functions" from our DL 190FormulaSheet. This strategy must be stated correctly for any credit to be given.)
Transcribed Image Text:4. Integrate: cos5 (30)sin² (30)do (State the strategy number you are using from the 6 strategies under "Powers of the Trig Functions" from our DL 190FormulaSheet. This strategy must be stated correctly for any credit to be given.)
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