# Crazy integration problem

## 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 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!!

Related Calculus and Beyond Homework Help News on Phys.org
gabbagabbahey
Homework Helper
Gold Member
What does the fundamental theorem of calculus say about:

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

???

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

gabbagabbahey
Homework Helper
Gold Member
Yep.

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