Wallis' formulas. 1) Prove the formula sin"-tx cos x n-1 S sin" x dx = S sin"-2x dx 2) Use that formula to prove prove Wallis' formulas: (n-1)(n-3)...(4)(2) n(n-2)...(5)(3)(1) | (n-1)(n-3)...(5)(3)(1) n(n=2)...(4)(2) ifn >1 is odd S/ ´sin"x dx = if n > 1 is even 3) Show how the substitution u = - x shows that S2 sin" x dx = S7² cos"x dx 4) Use the formula to find 2 sin'x dx and sin®x dx
Wallis' formulas. 1) Prove the formula sin"-tx cos x n-1 S sin" x dx = S sin"-2x dx 2) Use that formula to prove prove Wallis' formulas: (n-1)(n-3)...(4)(2) n(n-2)...(5)(3)(1) | (n-1)(n-3)...(5)(3)(1) n(n=2)...(4)(2) ifn >1 is odd S/ ´sin"x dx = if n > 1 is even 3) Show how the substitution u = - x shows that S2 sin" x dx = S7² cos"x dx 4) Use the formula to find 2 sin'x dx and sin®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...
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