# How to put set of data into integration?

It looks fundamental but I cannot find way to input a set of data into integration calculation. I need to get f value and f is defined as follows:

f=P*Exp[Integrate[(C-1)/P, {p, 0, p}]];
P={0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0};
C={-1337.49, -2675.98, -4014.47, -5352.96, -6691.44, -8029.93, -9368.42, -10706.9, -12045.4, -13383.9}
data = Transpose@{P, C}
{{0.5, -1337.49}, {1., -2675.98}, {1.5, -4014.47}, {2., -5352.96}, {2.5, -6691.44}, {3., -8029.93}, {3.5, -9368.42}, {4., -10706.9}, {4.5, -12045.4}, {5., -13383.9}}


I would like to find f value for each p and c data set.

• I think this would benefit by an explanation of what you are trying to do. As it is, this is very difficult to follow. Are you trying to do a finite Riemann sum with those lists? Or is it that you have an integrand which is a function of some parameters, and you want to do the integral for each of those parameters? Also note: your integration variable p does not appear in your integrand. Please give us more details. Commented Feb 1, 2017 at 21:38
• It seems you want to use Map. In addition to what march said, you should avoid capital names for your variables. The character C is already defined by Mathematica, which will lead to problems. Commented Feb 1, 2017 at 22:10
• Sorry for giving confusion. What I want is to get f value (f=P*exp[Integrate[(C-1)/P]dP from 0 to P) and I want to input P and its corresponding C value. That's why I made a pair of P and C. I can do it manually by putting for example P=0.5 and C=-1337.49 but I'm looking for if there is a good way to input P and C pair into the f equation to get f value for each pair.
– Sean
Commented Feb 2, 2017 at 2:45
• your f expression simply makes no sense. You need to fix that first before worrying about applying it to lists. Commented Feb 2, 2017 at 12:56

p = {0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0};
c = {-1337.49, -2675.98, -4014.47, -5352.96, -6691.44, -8029.93,
-9368.42, -10706.9, -12045.4, -13383.9};

data = Transpose[{p, c}];

f[p_, c_] := p*Exp[Integrate[(c - 1)/p, {t, 0, p}]]


Use Apply at level 1

results = f @@@ data

(*  {2.512747917061579*10^-582, 2.525560837878922*10^-1163,
1.903829320439066*10^-1744, 1.275691509165536*10^-2325,
8.094267261094953*10^-2907, 4.881324768115008*10^-3488,
2.861959016839073*10^-4069, 1.660264261598790*10^-4650,
9.29320921611432*10^-5232, 5.137586860445090*10^-5813}  *)