for v= -1/2 cos (2x) where is -1/2 coming from?In the final answer, where does 1/4 come from? b) √x sin (2x) dxIntegration by partsfdv =√ sin (2x) dxV = = = = 006 (2x)= (x) (¯ ½ cox (2x)) - √ ( = cos (2x)) (1 dx)1111U=Xdu= 1 dx- 1/2 × cos (2x) + = =√ √ cos (2x) dx-=—=/2 x cos(2x) + = sin(2x) + C

Solution ⇒ Given function ∫udv=∫x×sin⁡(2x) here u=xanddv=sin⁡(2x)…

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for v= -1/2 cos (2x) where is -1/2 coming from? In the final answer, where does 1/4 come from?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

for v= -1/2 cos (2x) where is -1/2 coming from?

In the final answer, where does 1/4 come from?

b) √x sin (2x) dx
Integration by parts
fdv =√ sin (2x) dx
V = = = = 006 (2x)
= (x) (¯ ½ cox (2x)) - √ ( = cos (2x)) (1 dx)
11
11
U=X
du= 1 dx
- 1/2 × cos (2x) + = =√ √ cos (2x) dx
-=—=/2 x cos(2x) + = sin(2x) + C

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