Explanation Given information: The integral is given as ∫ sin 8 θ cos θ d θ . Formula used: When a substitution is performed using differentials the change of variable formula is used. ∫ f ( u ( x ) ) u ' ( x ) d x = ∫ f ( u ) d u The power rule of indefinite integrals. ∫ x n d x = x n + 1 n + 1 + C when n ≠ ( − 1 ) Calculation: It is needed to change the variable in the integral. Hence, suppose that u = sin θ , Then the derivative of u is found to be, d u d θ = d ( sin θ ) d θ = cos θ d u = cos θ

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 5.7, Problem 52E

To determine

To find: The integration of sin8θcosθ with respect to θ .

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Chapter 5.7, Problem 51E

Chapter 5.7, Problem 53E

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Chapter 5 Solutions

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The integration of sin 8 θ cos θ with respect to θ .

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Chapter 5 Solutions