Find a best estimate for Integral of 0 to 10 f(x)g'(x)dx if f(x)=x^2 and g(x) has the values in the table below:
x: 0 2 4 6 8 10
g(x): 2.1 3.2 4.3 5.6 5.8 6.2
What I'm trying to do:
I'm did integration by parts and got:
f(x)g(x) - [integral] f'(x)g(x)dx
Using f(x) = x^2 I can get:
(x^2)g(x) - 2[integral] xg(x)dx
From here I'm thinking I'm thinking I can use simpsons rule to estimate. I'm just lost at what to do next
x: 0 2 4 6 8 10
g(x): 2.1 3.2 4.3 5.6 5.8 6.2
What I'm trying to do:
I'm did integration by parts and got:
f(x)g(x) - [integral] f'(x)g(x)dx
Using f(x) = x^2 I can get:
(x^2)g(x) - 2[integral] xg(x)dx
From here I'm thinking I'm thinking I can use simpsons rule to estimate. I'm just lost at what to do next
