I am having difficulty integrating

square root((1+x^3)) from x=0 to x=2

when n=4

I know the widths are 0,1/2,1,3/2,2

But I am having trouble setting it up.

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- Aug 25th 2011, 08:22 AMhomeylova223Numerical integration?
I am having difficulty integrating

square root((1+x^3)) from x=0 to x=2

when n=4

I know the widths are 0,1/2,1,3/2,2

But I am having trouble setting it up. - Aug 25th 2011, 08:35 AMPlatoRe: Numerical integration?
Let $\displaystyle f(x)=\sqrt{1+x^2}$ and $\displaystyle \Delta=0.5$.

Left hand sum $\displaystyle \sum\limits_{k = 0}^3 {f\left( {k\Delta } \right)\Delta } $.

Right hand sum $\displaystyle \sum\limits_{k = 1}^4 {f\left( {k\Delta } \right)\Delta } $.

Mid-point hand sum $\displaystyle \sum\limits_{k = 0}^3 {f\left( {\frac{2k\Delta+\Delta }{2} \right)\Delta } $. - Aug 25th 2011, 08:44 AMhomeylova223Re: Numerical integration?
I forgot to mention I have to use the trapezoid rule and I set it up like this.

((2/8)) times (1)(1+(0)^3)+(2)(1+(1/2)^3)+(2)(1+(1)^3)+(2)(1+(3/2)^3)+(1)(1+(2)^(3) - Aug 25th 2011, 10:51 AMSironRe: Numerical integration?
It looks fine if you don't forget to take the square root of the seperated terms because $\displaystyle f(x)=\sqrt{1+x^3}$.

- Aug 25th 2011, 12:52 PMhomeylova223Re: Numerical integration?
Thanks now I see the error of my calculus.

- Aug 25th 2011, 01:00 PMSironRe: Numerical integration?
You're welcome! :)