part 1 of 3 (i) Express the improper integral S 3xe-x/2 dx I = as lim It with each It a proper integral. t→∞

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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Question
part 1 of 3
(i) Express the improper integral
3xe-x/2 dx
I
=
S
3
as lim It with each It a proper integral.
t→∞
part 2 of 3
(ii) Compute the value of It.
✓ 1. I =
O
2. I
3. I =
4. I =
1. It
2. It
=
3. It
4. It
5. I = lim
5. It
=
=
=
lim
t→∞ √3
=
lim
t→∞
lim
t→∞
lim
t →∞
S.
S
t→∞ J-t
3.re~/2 dr
3xe-x/2 dx
3xe-x/2 dx
3.re e-x/t dx
3xe-x/2 dx
30e¯ +6(t+2)e-t/2
5e-²-(t+2)e-t/2
-30e-+6(t+2)e-t/2
6(3- t){e-² - e-t/²}
30e - 6(t+2)e-¹/²
Transcribed Image Text:part 1 of 3 (i) Express the improper integral 3xe-x/2 dx I = S 3 as lim It with each It a proper integral. t→∞ part 2 of 3 (ii) Compute the value of It. ✓ 1. I = O 2. I 3. I = 4. I = 1. It 2. It = 3. It 4. It 5. I = lim 5. It = = = lim t→∞ √3 = lim t→∞ lim t→∞ lim t →∞ S. S t→∞ J-t 3.re~/2 dr 3xe-x/2 dx 3xe-x/2 dx 3.re e-x/t dx 3xe-x/2 dx 30e¯ +6(t+2)e-t/2 5e-²-(t+2)e-t/2 -30e-+6(t+2)e-t/2 6(3- t){e-² - e-t/²} 30e - 6(t+2)e-¹/²
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