Calculating the value of an integral given some properties

**jmstudent** · Nov 18th 2010, 01:50 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, 02:02 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, 02:13 PM

Thanks a lot!

Thread: Calculating the value of an integral given some properties

LinkBack

Thread Tools

Display

Calculating the value of an integral given some properties

Similar Math Help Forum Discussions

Calculating integral

Integral properties

need help calculating this integral

Integral Properties

Integral properties

Search Tags