Hi,
During some calculations I came across a simple but strange integration problem. Two terms of this complicated equation can be given in simplified form as follows -
(1) I1 = Integrate[y, {x, X1, X2}]
(2) I2 = Integrate[1, {x, X1, X2}, {y, Y1, Y2}]
.Where y is not a function of x but at two extreme values of x (X1 and X2) it has different values (say Y1 and Y2). Now my problems are
whether consider y as a constant in this integration or not ? If I do (which seems reasonable), then my final result of I1 would be y(X2-X1), but y is not a real parameter and I assumed it for the sake of calculation and I need the solution of I1 & I2 in terms of X1, X2, Y1 and Y2.
If I consider y also as a variable and apply the limits (Y1 & Y2), my solution for I1 would be (Y2-Y1)*(X2-X1). Would it be correct to do so as I1 is integral over x only ??
Also if I apply the limits for both x and y, then solutions to both I1 and I2 would be (Y2-Y1)*(X2-X1). Is it justified to have same solution for I1 and I2.
I will really appreciate any suggestion on this weird problem. Thanks. SG
Thanks for replying, but y is not a function of x. If so, one would be able to express y in terms of x and integrate it in normal way. Would wait for your further suggestion.
Perhaps I am not able to put it correctly, let me try to give a parallel example. Let the population of world in 1980 and 2000 were respectively X1 and X2. Also in same two years respectively Y1 and Y2 planes were crashed all over the world. Now we can say that the year in which population was X1, Y1 plane crashes took place..but can we claim that number of plane crashes is the function of population ?
Well, one could say, more people, more flights, more crashes. that suggests that the number of crashes is indeed some sort of function of population. question is, how does it look like?
and which role plays your integral? counting the total number of crashes?