Recall that I(n) = (1 - x²)"dr. == 2.1 Substitute x = sin(t) in I(n) and show that I(n) can be written as I(n) = √12 π/2 (cos(t))2n+1dt -π/2 2.2 Now that we have I(n) = f(cos(t))2n+1dt. What is I(n - 1)? Leave your answer in integral form.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Recall that I(n) =
2.1 Substitute x =
(1 - x²)"dr.
sin(t) in I(n) and show that I(n) can be written as
I(n) = √12
π/2
(cos(t))2n+1dt
-π/2
2.2 Now that we have I(n) = f(cos(t))2n+1 dt. What is I(n - 1)?
Leave your answer in integral form.
Transcribed Image Text:Recall that I(n) = 2.1 Substitute x = (1 - x²)"dr. sin(t) in I(n) and show that I(n) can be written as I(n) = √12 π/2 (cos(t))2n+1dt -π/2 2.2 Now that we have I(n) = f(cos(t))2n+1 dt. What is I(n - 1)? Leave your answer in integral form.
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