Hi
I am trying to perform definite double integrals on an expression. If I run
Integrate[x^2 + y^2 + xy, {x, 0.0001, 0.01}, {y, 0.01, 0.5}]
in Mathematica v9.0.1.0 I get an expression as output:
0.00041266 + 0.004851 xy
However, if I run the same thing in wolframalpha:
then I get a numeric output: 0.000418907
Am I doing something wrong in Mathematica?
Many thanks
Gib
I believe that what you actually want to do is this:
Integrate[x^2 + y^2 + x y, {x, 0.0001, 0.01}, {y, 0.01, 0.5}]
Note that there is whitespace between the x and y at the end of the integrand. That whitespace is necessary - if the whitespace is not there, Mathematica will interpret your input as the single symbol xy. With whitespace, you get the symbol x multiplied by the symbol y.
I get 0.000418907 once I add the whitespace in Mathematica.
The integral can be done symbolically
Integrate[x^2 + y^2 + x y, {x, 10^-4, 10^-2}, {y, 10^-2, 1/2}]
20945345421/50000000000000
N[%]
0.000418907