Question 007: Complete the following question involving Trigonometric Integrals Given the following integral of a trigonometric function raised to an odd power Ssin 5(4x) dx and its substitution information sin (4x) sin(4x) - [1 - cos2(4x3)] cos(4x) u' -4sin(4x) dx dx -4 sin(4x) and its simplified form Scos (9x) dk- S(1 - u2]2 du 4 Find the integral and plug back in all of the necessary trig functions. 1 cos(4x) + cos?(4x) - cos (4x) + C 20 -1 1 O -1 1 cos(4x) - 12 1 +. cos(4x)-금cos3(4x) +C 4 4 cos(4x) - cos?(4x) + cos (4x) + C 1 -cos (4x) + C 20 cos(4x) -

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 007: Complete the following question involving Trigonometric Integrals
Given the following integral of a trigonometric function raised to an odd power
S sin 5(4x) dx
and its substitution information
sin (4x)
[1- cos2(+x)]2
sin(4x) *
cos(4x)
u'
-4sin(4x)
dx
dx
-4 sin(4x)
and its simplified form
-1
J cos(9x) dx:
du
Find the integral and plug back in all of the necessary trig functions.
O -1
1
-cos(4x) + cos(4x) - cos (4x) + C
4
20
O -1
1
cos(4x) - cos?(4x) + C
12
cos?(ax) + cos (4x) + c
2 cos?(4x)
1
cos(4x) -
1
cos(4x) -
20
cos (4x) + C
Transcribed Image Text:Question 007: Complete the following question involving Trigonometric Integrals Given the following integral of a trigonometric function raised to an odd power S sin 5(4x) dx and its substitution information sin (4x) [1- cos2(+x)]2 sin(4x) * cos(4x) u' -4sin(4x) dx dx -4 sin(4x) and its simplified form -1 J cos(9x) dx: du Find the integral and plug back in all of the necessary trig functions. O -1 1 -cos(4x) + cos(4x) - cos (4x) + C 4 20 O -1 1 cos(4x) - cos?(4x) + C 12 cos?(ax) + cos (4x) + c 2 cos?(4x) 1 cos(4x) - 1 cos(4x) - 20 cos (4x) + C
Expert Solution
Step 1

For solving this integral, we have to make use of some substitution and we will also use the trigonometric identity 

cos2(x)+sin2(x)=1

 

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