4.19 Numerically integrate f(x,y) in 2D

Problem: Integrate

\[ \int _{7}^{10}\int _{11}^{14}\left ( x^{2}+4y\right ) dxdy \]

The exact answer is 1719

Mathematica

f[x_,y_] := x^2+4 y 
r = Integrate[f[x,y],{x,11,14},{y,7,10}]
 

Out[69]= 1719
 

 

Matlab

clear all; 
format long 
f=@(x,y) x.^2+4*y; 
integral2(f,11,14,7,10)
 

ans = 
     1.719000000000004e+03