Set Im = /2 0 sin m x dx. Use Exercise 69 to prove that Conclude

Question:

Set Im = ∫π/2sinm x dx. Use Exercise 69 to prove that

12m 12m+1 = 2m 12m3 2m 2m-2 2m 2m-2 2m + 1 2m 1 N!= KIN 2 2 2|3

Conclude that

KIN 2 2.2 4.4 1.3 3.5 2m. 2m 12m (2m 1)(2m + 1) I2m+1 -



Data From Exercise 69

Let I= ∫π/2sinx dx.

(a) Show that I= π/2 and I= 1.
(b) Prove that, for m ≥ 2,

Im = m-1 m -Im-2

(c) Use (a) and (b) to compute Im for m = 2, 3, 4, 5.

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Related Book For  book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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