how find integration area under the curve ?

i have a problem like this

the problem is how to find integration area under the function f(x), i had tried it with the simpson rule with applied the interpolation lagrange 3rd orde, but i could not found the integration formula in below picture

is my method true or not ? can anybody tell me about this ? thanks

Answer 1

[Wayne King]

I'm assuming that b=x_0 and a=x_3 -- is that correct? If that is correct, it looks like your expression above significantly overestimates the value of the definite integral of a function over the interval [a,b].

Compare the above to Simpson's rule

 \dfrac{b-a}{6} \{ f(a)+ 4f(\tfrac{a+b}{2})+ f(b) \}

And I'm not sure what this question has to do with MATLAB. Have you coded your rule and tried it as an approximation to several integrals to see whether it is systematically overestimating the true value?

[jakv]

i tried it with manual integration not used matlab or another software.