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1. The integral In -6.³ cos" t dt, where n is a non-negative integer. n-1 In-2, if n ≥ 2. n (b) Find an expression for I4 in terms of Io (or in terms of I₂ if you prefer), and thus determine 1.² (c) Find an expression for I7 in terms of I₁, and thus determine S (a) Use integration by parts to show that In cost dt. - cos7 t dt.

1. The integral In -6.³ cos" t dt, where n is a non-negative integer. n-1 In-2, if n ≥ 2. n (b) Find an expression for I4 in terms of Io (or in terms of I₂ if you prefer), and thus determine 1.² (c) Find an expression for I7 in terms of I₁, and thus determine S (a) Use integration by parts to show that In cost dt. - cos7 t dt.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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could you pleaae do all parts and could the answer be written out please , not typed up. Thank you 

1. The integral In = S.³ cos" t dt, where n is a non-negative integer. (a) Use integration by parts to show that In cos4 t dt. = n -In-2 In-2, if n ≥ 2. n (b) Find an expression for I in terms of Io (or in terms of I₂ if you prefer), and thus determine 플 [² (c) Find an expression for I7 in terms of I₁, and thus determine 0 cos7 t dt.
Transcribed Image Text:1. The integral In = S.³ cos" t dt, where n is a non-negative integer. (a) Use integration by parts to show that In cos4 t dt. = n -In-2 In-2, if n ≥ 2. n (b) Find an expression for I in terms of Io (or in terms of I₂ if you prefer), and thus determine 플 [² (c) Find an expression for I7 in terms of I₁, and thus determine 0 cos7 t dt.
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