# Multiplying two sets of data (x,y values, but different x density) followed by integration of the product

I've been trying to do this by myself today, but no luck yet. Please, see attached image.

Basically, I do have two data sets A (x1,y1) and B (x2,y2). Please, note that x1 and x2 have different range and density. Say x1 goes like 200, 201, 202... but x2 goes like 180, 180.5,181,181.5..

There is two tasks I would like to write a code using Mathematica:

1. Find the product of multiplying of two different set (c).
2. Calculate the integration of the product and compared to that of the original (x1,y1) (A).

Because these two data sets have different range and density, I was thinking about using Interpolation[], but I feel like there should be a simpler way to do this job done.

The 1st data set looks like this:

{{Baseline 100%T,},{Wavelength (nm),%T},{2500,27.0365},{2499,27.1329},{2498,27.0761},{2497,27.2015},{2496,27.2032}, ...2289... ,{206,58.9478},{205,59.2311},{204,59.4642},{203,59.7953},{202,59.6811},{201,59.7263},{200,60.0759}}


The 2nd data set looks like this:

{{Wave length,Spectral irradiance},{280,2.54*10^-26},
{280.5,1.09*10^-24}, ...1698... ,{2490,0.0035},{2500,0.00703}}

• What do you mean by "multiplying of two different sets"? Could you give a simple example of the operation you have in mind? – Alexei Boulbitch Apr 29 '15 at 8:15