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Crazy integration problem

  • Thread starter Spartan029
  • Start date
  • #1
15
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Homework Statement



Let [tex]f[/tex] be twice differentiable with [tex]f(0)=6, f(1)=5, [/tex] [tex] f'(1)=2[/tex]
Evaluate the integral [tex]\int_0^{1}x f''(x) dx[/tex]


Homework Equations



[tex] \int uv' dx = uv = \int u'v dx [/tex]

The Attempt at a Solution



u = x and v' = f''(x)
so
u' = 1dx and v = f'(x)
so

[tex]xf'(x) - \int_0^{1}f'(x) dx[/tex]

from here im not sure what to do... maybe parts again...
u = 1dx and v' = f'(x)
so
u' = 0? and v = f(x) //derivative of 1dx is 0 right?
so

[tex]xf'(x) - f(x) - \int_0^{1} 0 dx[/tex] ???

i really dont know. any help would be awesome!!
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6
What does the fundamental theorem of calculus say about:

[tex]\int_0^1 f'(x)dx[/tex]

???:wink:
 
  • #3
15
0
[tex]\int_0^1 f'(x)dx = f(1) - f(0)[/tex] ??
 
  • #4
gabbagabbahey
Homework Helper
Gold Member
5,002
6
Yep.
 
  • #5
15
0
wow thats awesome. now i feel retarded haha.
but seriosuly... thanks gabba!!
 

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