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posted by  Novaworks on 11/3/2009 3:04:55 PM  |  status: Closed  |  Earned Karma: 1145

Antiderivative...

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Calculus N/A N/A N/A 11/4/2009 at 6:00:00 PM
Question Details:
Find the most general antiderivative of the function. Use C for any needed constant.
f(x) = 5√x + 3cos(x)
F(x) = ?
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Sage
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posted by rimantas on 11/3/2009 3:24:25 PM  |  status: Live
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Response Details:
f(x) = [5√x] + 3cosx      to find the most general antiderivative
F(x) = 10x^(3/2) + 3sinx + C   is the most general antiderivative of the given function
hope this helps
Oracle
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posted by Sonny's on 11/3/2009 6:22:15 PM  |  status: Live
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Response Details:
Given the f(x) function:

 
Integrate both sides of the function.

 
Use the following integration formulas:
1)  (Power Rule of Integration)
2)  (Integration Formula for cos(x))

 

 
Simplify by multiplying

 
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Oracle
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posted by Marth on 11/3/2009 6:54:44 PM  |  status: Live
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Response Details:


We can write this as .

==.
By Power Rule, .


So we have = (we can combine the constants).


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