Do you know how to solve an integral over a loop?

Hi, I have a integral that I need to solve, the problem is that I have a loop, that is, for each value of r, Ihave one U, my inputs are:

r=[0 2.19 4.53 6.87 9.21 11.55 13.89 16.23 18.57 20.95 23.29 25.63 27.97 30.31 32.66 35.0 37.34 39.68 42.023 44.36 46.70 49.04 51.38];

U=[0 0 0 0.588 1.685 2.03 2.307 2.544 2.598 2.733 2.565 2.663 2.437 2.425 2.263 2.507 2.525 2.537 2.416 2.268 1.979 1.708 0.614];

Function is: F=2/(r^2) ∫U r dr

The bounds of integral are between 0 to 51.38 . Any help would be appreciated.

[Walter Roberson]

It does not make sense to integrate with respect to r if you have one U value for each r value.

It does not make sense to integrate with respect to a discrete variable.

Answer 1

[Torsten]

Ur=U.*r;
result=trapz(r,Ur);

gives you an approximation of

integral_{r=0}^{r=51.38} U*r dr.

Best wishes

Torsten.