1. ## Numerical 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.

2. ## Re: Numerical integration?

Originally Posted by homeylova223
I am having difficulty integrating

square root((1+x^3)) from x=0 to x=2 when n=4
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 $\displaystyle \sum\limits_{k = 0}^3 {f\left( {\frac{2k\Delta+\Delta }{2} \right)\Delta }$.

3. ## Re: 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)

4. ## Re: Numerical integration?

It looks fine if you don't forget to take the square root of the seperated terms because $\displaystyle f(x)=\sqrt{1+x^3}$.

5. ## Re: Numerical integration?

Thanks now I see the error of my calculus.

6. ## Re: Numerical integration?

You're welcome!