Integrating with Multiple Variables: How to Solve the Crazy Integration Problem?

[Spartan029]

Homework Statement

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

Homework Equations

\int uv' dx = uv = \int u'v dx

The Attempt at a Solution

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

xf'(x) - \int_0^{1}f'(x) dx

from here I am 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

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

i really don't know. any help would be awesome!

 

[gabbagabbahey]

What does the fundamental theorem of calculus say about:

\int_0^1 f'(x)dx

?

 

[Spartan029]

\int_0^1 f'(x)dx = f(1) - f(0) ??

 

[gabbagabbahey]

Yep.

 

[Spartan029]

wow that's awesome. now i feel retarded haha.
but seriosuly... thanks gabba!