# symbolic and numeric double integration method

fidbc corrected some of my previous code for double integration. However I am only able to good a good numerical double integral. Is their a sage method that can do both symbolic ie variables as bounds and numeric integration if not what is the symbolic integration method. Using the current integrate method I have I get back the wrong results in bracketed around the word integrate.

Here is my double integration code corrected by fidbc for numerical integration does anyone know a better integration method or methods for symbolic double integration.

```
from sage.plot.plot3d.shapes import Box
x,y = var('x,y')
@interact
def interplay(function= input_box(sin(x*y)),lower_x_bound= input_box(0),upper_x_bound = input_box(1),lower_y_bound=input_box(0),upper_y_bound=input_box(1),dydx = checkbox(default = False)):
if dydx==False :
prev = integral(function,x,lower_x_bound,upper_x_bound)
result = n(integral(prev,y,lower_y_bound,upper_y_bound))
q ="$\int_%s^{%s} \int_%s^%s %s \,dx\,dy = %s $" % (lower_y_bound, upper_y_bound,lower_x_bound,upper_x_bound,function,result)
else:
result = n(integral(integral(function,y,lower_y_bound,upper_y_bound),x,lower_x_bound,upper_x_bound))
q = "$\int_%s^{%s} \int_%s^%s %s \,dy\,dx = %s $" % (lower_x_bound,upper_x_bound,lower_y_bound,upper_y_bound,function,result)
html("%s" %q)
```

Can you define what you mean by good? Do you mean one that won't return integrate(....)? It seems that sage will always return integrate(...) when there is no closed form solution.

If what you want is the closed form solution when that is avaliable and a numeric solution the following function should suffice: