Thread: Calculating the value of an integral given some properties

Hi, I have done all the exercises I have to do for tomorrow, but I am stuck on this one...my professor said it is really easy, but I have no clue how to solve this . Any help would be very much appreciated, thanks!

Given the following:
$\displaystyle u(a)=-4, u'(b)=-4, u'(a)=-1, u(b)=-4$
$\displaystyle v'(a)=-8, v(b)=3, v(a)=4, v'(b)=2$

$\displaystyle \int^b_a u(x) v(x) dx = 4, \int^b_a u(x) dx = 3$
$\displaystyle \int^b_a v'(x) dx = -1, \int^b_a u'(x) v(x) dx = -6$

What is the value of $\displaystyle \int^b_a u(x) v'(x) dx$?

By by-parts:

$\displaystyle \displaystyle \int_{a}^{b}u(x)v'(x)\;{dx} = u(x)v(x)\bigg|_{a}^{b}-\int_{a}^{b}u'(x)v(x)\;{dx} $

Thanks a lot!