Double integration of e^(xy)!!!!!?

Question

How do you find the double integration of e^(xy)?
- bounded from 0- order of dx and dy is unimportant

THANKSSSS!!!!

Answer 1

Pick which one you prefer to do first, doesn't matter.



I'm going to choose to do dx first.



Replace y with a constant, b, if you have to, in order to see that it is not being treated as a variable.



∫ e^(bx) dx[0,1]



Integrate normally:



(1/b)e^(bx) [0,1]

(1/b)e^b - 1/b



And substitute back for y.



(1/y)e^y - 1/y



Now you can integrate dy.



∫ [(1/y)e^y - 1/y] dy[0,1]



Unfortunately, there is no way to integrate (e^y)/y manually, a formula was developed for just this situation, called the exponential integral, abbreviated with the function Ei(...).



The integral becomes:



Ei(1) - γ ~ 1.3179021514544038948600088442492318379749012457927839928404611969976461077561394826119536468343922075



Where γ is the Euler-Mascheroni Constant ~ 0.5772156649015328606065120900824024310421593359399235988057.

Answer 2

think you prefer to be certain the area between the curves y = x^2 and y = x^3 from x = a million to x= 3. this is finished via the double imperative Int (x=0 to a million) Int (y = x^2 to x^3) dy dx

Answer 3

Ans



1.3179