Let In x n cos(x 2 ) dx and J n x n sin(x 2 ) dx (a) Find a reduction formula that expresses I, in terms of Jn 2 Write x cos(x) as x 1(x cos(x)) (b) Use the result of (a) to show that I, can be evaluated explicitly if n is odd (c) Evaluate 13 ...

a Integration by Parts with u x1 and dv x cosx dx yields n 1 1 In x sinx ...

Let In = x n cos(x 2 ) dx and J n = x n sin(x 2

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Let In = ∫xⁿcos(x²) dx and J_n= xⁿsin(x²) dx.

(a) Find a reduction formula that expresses I, in terms of Jn-2. Write x" cos(x) as x-1(x cos(x)). (b) Use

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 01, 2023 08:03 AM

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Let In = x n cos(x 2 ) dx and J n = x n sin(x 2

Question:

(a) Find a reduction formula that expresses I, in terms of Jn-2. Write x" cos(x²) as x-1(x cos(x²)). (b) Use the result of (a) to show that I, can be evaluated explicitly if n is odd. (c) Evaluate 13.

Step by Step Answer:

a Integration by Parts with u x1 and dv x cosx dx yields n 1 1 In x sinx ...View the full answer

Calculus

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