Explanation Given information: The integrals are ∫ 0 π sin m x sin n x d x = 0 , ∫ 0 π cos m x cos n x d x = 0 and ∫ 0 2 π sin m x cos n x d x = 0 . Formula used: The formulas are: sin m x sin n x = 1 2 [ cos ( m x − n x ) − cos ( m x + n x ) ] cos m x cos n x = 1 2 [ cos ( m x − n x ) + cos ( m x + n x ) ] sin m x cos n x = 1 2 [ sin ( m x − n x ) + sin ( m x + n x ) ] Calculation: Consider m and n are integers with m ≠ ± n . Solve the integral ∫ 0 π sin m x sin n x d x . ∫ 0 π sin m x sin n x d x = ∫ 0 π 1 2 [ cos ( m x − n x ) − cos ( m x + n x ) ] d x = 1 2 [ sin ( m − n ) x ( m − n ) − sin ( m + n ) x ( m + n ) ] 0 π Substitute the limits. 1 2 [ sin ( m − n ) x ( m − n ) − sin ( m + n ) x ( m + n ) ] 0 π = 1 2 [ sin ( m − n ) π ( m − n ) − sin ( m + n ) π ( m + n ) − sin ( m − n ) 0 ( m − n ) + sin ( m + n ) 0 ( m + n ) ] = 1 2 [ 0 ( m − n ) − 0 ( m + n ) − 0 ( m − n ) + 0 ( m + n ) ] = 0 Solve the integral ∫ 0 π cos m x cos n x d x . ∫ 0 π cos m x cos n x d x = ∫ 0 π 1 2 [ cos ( m x − n x ) + cos ( m x + n x ) ] d x = 1 2 [ sin ( m − n ) x ( m − n ) + sin ( m + n ) x ( m + n ) ] 0 π Substitute the limits

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 7.2, Problem 73E

To determine

The orthogonality relations between the equations ∫0πsinmxsinnx dx=0, ∫0πcosmxcosnx dx=0 and ∫02πsinmxcosnx dx=0.

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Chapter 7.2, Problem 72E

Chapter 7.2, Problem 74E

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Please help on both Part b) and c) below Thanks

find the zeros of the function algebraically: f(x) = 9x2 - 3x - 2

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Chapter 7 Solutions

Calculus: Early Transcendentals

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The orthogonality relations between the equations ∫ 0 π sin m x sin n x d x = 0 , ∫ 0 π cos m x cos n x d x = 0 and ∫ 0 2 π sin m x cos n x d x = 0 .

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The orthogonality relations between the equations ∫0πsinmxsinnx dx=0, ∫0πcosmxcosnx dx=0 and ∫02πsinmxcosnx dx=0.

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