# Crazy integration problem

1. Sep 29, 2008

### Spartan029

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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 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

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

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

2. Sep 29, 2008

### gabbagabbahey

What does the fundamental theorem of calculus say about:

$$\int_0^1 f'(x)dx$$

???

3. Sep 29, 2008

### Spartan029

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

4. Sep 29, 2008

### gabbagabbahey

Yep.

5. Sep 29, 2008

### Spartan029

wow thats awesome. now i feel retarded haha.
but seriosuly... thanks gabba!!