Explanation The provided integral is, 4 ∫ sin x cos x d x = − cos 2 x + C Rewrite. 2 ∫ 2 sin x cos x d x = − cos 2 x + C Use the formula for 2 sin x cos x = sin 2 x to simplify the above expression. 2 ∫ sin 2 x d x = − cos 2 x + C Rewrite. ∫ ( sin 2 x ) 2 d x = − cos 2 x + C Let u = 2 x . Differentiate the above considered function. d u = 2 d x Substitute u for 2 x and d u for 2 d x

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8.5, Problem 68E

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Whether the provided statement “4∫sinxcosxdx=−cos2x+C” is true or false.

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Chapter 8.5, Problem 67E

Chapter 8, Problem 1RE

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 8 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 8.1 - For each angle, find a coterminal angle such that...Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 1SWU Ch. 8.1 - Prob. 2SWU Ch. 8.1 - Prob. 3SWU Ch. 8.1 - Prob. 4SWU Ch. 8.1 - Prob. 5SWU Ch. 8.1 - Prob. 6SWU

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Whether the provided statement “ 4 ∫ sin x cos x d x = − cos 2 x + C ” is true or false.

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Whether the provided statement “4∫sinxcosxdx=−cos2x+C” is true or false.

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Chapter 8 Solutions