Originally Posted by

**spatran029** **1. The problem statement, all variables and given/known data**

Estimate $\displaystyle \int_{0}^{10} f(x) g'(x) dx $ for f(x) = $\displaystyle x^{2}$

and g has the values in the following table.

$\displaystyle

\begin{array}{|l | c|c|c|c|c|c |}

\hline g&0&2&4&6&8&10\\

\hline g(x)&2.3&3.1&4.1&5.5&5.9&6.1\\

\hline

\end{array}

$

**2. Relevant equations**

$\displaystyle \int uv' dx = uv = \int u'v dx $

**3. The attempt at a solution**

Okay so, since f(x) is x squared i chose

u = $\displaystyle x^{2}$ and v' = g'(x)

&

u' = 2x dx and v = g(x)

plugging in...

$\displaystyle g(x)x^{2} - \int_{0}^{10} 2xg(x) dx $

and this is where im stuck. I cant plug in the g values because i first need to take the integral of 2xg(x) ....I think. lol

a nudge in the right direction would be ub3r helpful and much appreciated. thanks!