Is the following what you want? You're given a table of pairs {f,C2} and you want to end up a table of pairs {f,(2*Integrate[C2])^0.5} ? If so, the following should work:

(* Create an example table where there are pairs {f,C1} *)
a = 5/100;
U = 13200;
L = 100;
C1 = Exp[-a (2 \[Pi] f \[Xi])/U ] * Cos[(2  \[Pi]  f \[Xi])/U]
C2 = Table[{f, C1}, {f, 0, 1000, 5}]

(* Take the table of pairs of {f,C1} and create a table of pairs \
{f,(2*Integrate[C1^0.5])^0.5} *)
C3 = Table[{C2[[i, 
     1]], (2 NIntegrate[C2[[i, 2]]^0.5, {\[Xi], 0, L}])^0.5}, {i, 
   Length[C2]}]

(When you say in your Notebook that the X's aren't right, is that because the X's (or rather your values for f) were integrated, too?)

Anton ,

I have installed 10.01 and transferred my nb that is in V5.2 to the 10.01version. I have included that nb.

luke

PS basically I'm trying to integrate a table of functions and then plot table of (x,y) numbers. During this process the x values must remain the same.

Attachments:

Luke, I think we are using different versions of Mathematica. What is your version?

Jim, Thanks, I have attached a file that I hope clarified the definition of the problem. In addition I have completed more calculation to show various features to save others from having to do that. I don't think this should have a "vote of 1" yet. I don't feel that the concerns are understood.

thanks luke

Attachments:

I think the integral you want can be integrated explicitly:

L=.;
a=.;
f=.;
U=.;
c2 = Exp[-a(2\[Pi] f \[Xi])/U ] * Cos[(2  \[Pi]  f \[Xi])/U]
integral = Integrate[c2^2 \[Xi],{\[Xi],0,L}]

with the following result

E^(-((2 a f \[Pi] \[Xi])/U)) Cos[(2 f \[Pi] \[Xi])/U]

(U (a^2 (-1+a^2) U+(1+a^2)^2 U-E^(-((4 a f L \[Pi])/U)) ((1+a^2)^2 (4 a f L \[Pi]+U)+a^2 (4 a (1+a^2) f L \[Pi]+(-1+a^2) U) Cos[(4 f L \[Pi])/U]-2 a^2 (2 (1+a^2) f L \[Pi]+a U) Sin[(4 f L \[Pi])/U])))/(32 a^2 (1+a^2)^2 f^2 \[Pi]^2)

Then a table could be constructed with (2*integral)^0.5.

How about something like either the two ways below? One uses Map and the other uses Table.

L = 100
f[z_] := NIntegrate[z, {x, 0, L}]
t = {{1, Exp[-0.1 x] Cos[2.3 x]}, {2, Exp[-0.2 x] Cos[4.3 x]}}
Map[f, t[[All, 2]]]
Table[NIntegrate[t[[i, 2]], {x, 0, L}], {i, Length[t]}]

This is a reply to all ---Thanks I provided equations as examples; do not want to apply equations in the integral.

My input (integrand) to the integral is a "Table"; see the Table at the end of the example in nb. I want to input a similar table into the integral; the table could have 500 (X, Y) terms; don't want to do this term by term. The "X" part is not effected by the integration; only the "Y" part. After integration only a table of (X,Y) terms (numbers) will remain. I'm going to do this about 150 times.

My customer provides me a the "table" which is a cross power spectral density and this integrated result is a generalize force.