Evaluate the integral. 39 sin(40) de
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Evaluate the integral.
sin(48) de
Step 1
We will begin by letting u = sin(48) and dv = e38 de.
Then du = sin 40
4 cos(40)
de and v =
3
Step 2
After integration by parts we have
sin (40)e39
38
sin(48) de =
0 sin(40)
4/3
4/3
38
cos(48) de.
Step 3
We'll now apply the integration by parts procedure to the new integral
30
cos(40) de, letting U = cos(4e)
and dV = e3 de.
30
Then du = -4 sin( 40)
-4 sin(40)| de and v =
Step 4
After integration by parts we have
36 cos (40)
1
cos(40)
|-4/3
30
cos(48) de
-4/3
sin(48) de.
Step 5
Notice that the original integral
38
sin(48) de is once again present. In fact, putting together all our work
so far, if we let I =
·글e38 sin(46)
139 cos(48) +
4 [1.30
글 + Gr
+ C,.
30
sin(48) de. we have I =
This can be re-arranged to give us
I = Le39 sin(48) -
e3° cos(48) -
]I+ c,.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d88a89c-4743-486c-903a-d25a9887f98a%2F91eeb78f-71aa-4151-8fbe-1140069bbdb0%2Fprlhc1y_processed.png&w=3840&q=75)
Transcribed Image Text:Evaluate the integral.
sin(48) de
Step 1
We will begin by letting u = sin(48) and dv = e38 de.
Then du = sin 40
4 cos(40)
de and v =
3
Step 2
After integration by parts we have
sin (40)e39
38
sin(48) de =
0 sin(40)
4/3
4/3
38
cos(48) de.
Step 3
We'll now apply the integration by parts procedure to the new integral
30
cos(40) de, letting U = cos(4e)
and dV = e3 de.
30
Then du = -4 sin( 40)
-4 sin(40)| de and v =
Step 4
After integration by parts we have
36 cos (40)
1
cos(40)
|-4/3
30
cos(48) de
-4/3
sin(48) de.
Step 5
Notice that the original integral
38
sin(48) de is once again present. In fact, putting together all our work
so far, if we let I =
·글e38 sin(46)
139 cos(48) +
4 [1.30
글 + Gr
+ C,.
30
sin(48) de. we have I =
This can be re-arranged to give us
I = Le39 sin(48) -
e3° cos(48) -
]I+ c,.
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