1. Integration bt parts help

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

Estimate $\int_{0}^{10} f(x) g'(x) dx$ for f(x) = $x^{2}$
and g has the values in the following table.

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

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

3. The attempt at a solution

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

u = $x^{2}$ and v' = g'(x)
&
u' = 2x dx and v = g(x)

plugging in...

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

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!

ps. that latex table took me like a half hour to figure out rofl

2. Originally Posted by spatran029
1. The problem statement, all variables and given/known data

Estimate $\int_{0}^{10} f(x) g'(x) dx$ for f(x) = $x^{2}$
and g has the values in the following table.

$
\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

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

3. The attempt at a solution

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

u = $x^{2}$ and v' = g'(x)
&
u' = 2x dx and v = g(x)

plugging in...

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

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!
use by parts again to integrate the 2xg(x)

ps. that latex table took me like a half hour to figure out rofl
haha, good job!

(i fixed it up a bit)

3. Originally Posted by Jhevon
use by parts again to integrate the 2xg(x)
but when i use v' = g(x) i dont know what v is.

and if i use u = g(x) and v' = 2x i end up wher i started. LOL

4. Originally Posted by spatran029
but when i use v' = g(x) i dont know what v is.

and if i use u = g(x) and v' = 2x i end up wher i started. LOL
just write it as $\int g(x)~dx$. you can get as estimate for this integral using the table.

5. oh right!! because were not looking for an exact value! thanks for helping me