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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!!