how can i solve numerically a vector integral?

I have a plot of gaussian alike profile in matlab.

the plot presents the intensity (I) profile( E^2) as a function of location(radius) r.

i need to calculate the integral of I(r)*r*dr which is the area under the graph, i tried solving with trapz but the answer isnt correct, so how can i calculate this integral when

I(r) is a vector and r is a value i know?

[madhan ravi]

integral() with arrayvalued option?

[Torsten]

trapz(r,I.*r) is too inexact ?

[Adi]

The intensity is normalized so i should get area under the graph= 1,

the plot looks like that

plot( r_vector,intensity_vector), so i tried trapz(r_vector,intensity_vector) to get the area under the graph is it correct? for this option the result is 1.7

thank you

[Torsten]

As I wrote,

trapz(r_vector,r_vector.*intensity_vector)

if you want to approximate

integral(I(r)*r*dr )

[Adi]

thank you!