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posted by  Howl on 11/6/2009 3:18:39 PM  |  status: Closed  |  Earned Karma: 0

Having some trouble with Integrals

Course Textbook Chapter Problem Needs by
Calculus Calculus (6th) by Stewart 8-9 N/A 11/9/2009 at 12:00:00 PM
Question Details:
(1)The first one I have trouble with because of the integral is from 0 to t. I let the x under the square root to equal asinθ and replugged it in tnto the equation and factored the a2 out leaving 1-sin2θ under the square root. I then substituted and got cos2θ under the square root and that's where I got stuck.
(2)This one I have no clue how to even start.
(3)Or this one.
(4)
For this one, I used my reference sheet from the book and got
I'm not sure if that's right or not.
Any help would be awesome.

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Sage
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posted by rimantas on 11/6/2009 3:46:23 PM  |  status: Live
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for 1) the easiest way is to expand and get a polynomial to integrate.
for 2)  use partial fractions
for 3) integrate by parts several times, but do not change boats in midstream, i.e.
       for the u part choose the polynomial part and for the dv part chose the exponential part
hope this helps
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posted by Howl on 11/6/2009 4:05:55 PM  |  status: Live
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Thanks for your reply. I just realized I must've deleted the first question by accident.  I'll try to figure those darn problems out. Still verrry confused about these equations. XD
Oracle
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posted by The Big Unit on 11/6/2009 4:27:25 PM  |  status: Live
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Response Details:

1)

Performing a u-substitution, you will have:
 so
So your integral becomes:
 (ANSWER)
2)
Taking the antiderivative yields:
 (ANSWER)
3)
Using partial fractions, you will have:
Equating coefficients yields:
Solving the above three equations simultaneously yields , , and . So you will have:
                                          
Jon AKA THE BIG UNIT
If you have any questions about the problem, just message me and I will help you out. Hope this helps!
 
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