Beyond the Basics - A Guide to MATLAB for Beginners and Experienced Users - page 63

You have another option. If you type double(int( )) , then Maple's
numerical integration routine will evaluate the integral — even over an
infinite range.
MATLAB can also do multiple integrals. The following command computes
the double integral
π sin x

( x 2 + y 2 ) dydx :

0 0

>> syms x y; int(int(xˆ2 + yˆ1, y, 0, sin(x)), 0, pi)

ans =
pi^2-32/9
Note that MATLAB presumes that the variable of integration in int is x
unless you prescribe otherwise. Note also that the order of integration is as in
calculus, from the “inside out”. Finally, we observe that there is a numerical
double integral command dblquad , whose properties and use we will allow
you to discover from the online help.

Limits

You can use limit to compute right- and left-handed limits and limits at
infinity. For example, here is lim
x → 0

sin( x ) / x :

>> syms x; limit(sin(x)/x, x, 0)

ans =
1
To compute one-sided limits, use the 'right' and 'left' options. For exam-
ple,

>> limit(abs(x)/x, x, 0, 'left')

ans =
-1
Limits at infinity can be computed using the symbol Inf :

>> limit((xˆ4 + xˆ2 - 3)/(3*xˆ4 - log(x)), x, Inf)

ans =
1/3