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posted by  crystalcakes on 11/4/2009 11:41:03 PM  |  status: Closed  |  Earned Karma: 0

antiderivitave

Course Textbook Chapter Problem Needs by
Calculus N/A N/A N/A 11/5/2009 at 1:00:00 AM
Question Details:
Find f.
f ''(t) = 3et + 5sin(t) 
f(0) = 0 
f(π) = 0

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posted by anonymousxyz on 11/5/2009 12:22:09 AM  |  status: Live
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Response Details:


f ''( t )  =  3et  +  5 sin t


f '( t )
          =  Integral  [  f '' ( t )  ]  dt

          =  Integral  [  3et  +  5 sin t  ]  dt

          =  3et  -  5 cos t  +  A


f( t )
        =  Integral  [  f '( t )  ]  dt

        =  Integral  [ 3et  -  5 cos t  +  A  ]  dt

        =  3et  -  5 sin t  +  At  +  B


f( 0 )  =  0  =>

3e0  -  5 sin 0  +  A( 0 )  +  B  =  0  =>

3  +  B  =  0  =>

B  =  -3  =>


f( t )  =  3et  -  5 sin t  +  At  -  3


f( π )  =  0  =>

3eπ  -  5 sin π  +  A( π )  -  3  =  0  =>

3eπ  +  Aπ  -  3  =  0  =>

Aπ  =  3  -  3eπ  =>

A  =  ( 3  -  3eπ ) / π  =>

f( t )  =  3et  -  5 sin t  +  [ ( 3  -  3eπ ) / π ]t  -  3
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