Calculating the value of an integral given some properties

**jmstudent** · Nov 18th 2010, 12:50 PM

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:
$u(a)=-4, u'(b)=-4, u'(a)=-1, u(b)=-4$
$v'(a)=-8, v(b)=3, v(a)=4, v'(b)=2$

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

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

**TheCoffeeMachine** · Nov 18th 2010, 01:02 PM

By by-parts:

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

**jmstudent** · Nov 18th 2010, 01:13 PM

Thanks a lot!

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