I need to find the integral from 1-4 of xf''(x)dx given that f(1)=2, f(4)=7, f'(1)=5, and f'(4)=3. I'm not sure how to begin. When I've done this sort of thing before I always had the function.
$\displaystyle \int x \cdot f''(x) \, dx$
$\displaystyle u = x$
$\displaystyle du = dx$
$\displaystyle dv = f''(x) \, dx$
$\displaystyle v = f'(x)$
$\displaystyle x \cdot f'(x) - \int f'(x) \, dx = x \cdot f'(x) - f(x)$
now use the FTC to determine the value of the definite integral.