# Multiple Integrals; Reference - HP 50g User Manual

Graphing calculator.

To define the functions f(x,y) and g(x,y,z), in ALG mode, use:
DEF(f(x,y)=x*COS(y)) `
To type the derivative symbol use ‚¿ . The derivative
for example, will be entered as x(f(x,y)) ` in ALG mode in the screen.

## Multiple integrals

A physical interpretation of the double integral of a function f(x,y) over a
region R on the x-y plane is the volume of the solid body contained under
the surface f(x,y) above the region R. The region R can be described as R
= {a<x<b, f(x)<y<g(x)} or as R = {c<y<d, r(y)<x<s(y)}. Thus, the double
integral can be written as
∫∫
(
, x
R
Calculating a double integral in the calculator is straightforward.
double integral can be built in the Equation Writer (see example in
Chapter 2 in the user's guide), as shown below. This double integral is
calculated directly in the Equation Writer by selecting the entire expression
and using function @EVAL . The result is 3/2.

### Reference

For additional details of multi-variate calculus operations and their
applications see Chapter 14 in the calculator's user's guide.
b
( g
) x
∫ ∫
) y
dA
(
a
( f
) x
DEF(g(x,y,z)= (x^2+y^2)*SIN(z) `
d
( s
∫ ∫
, x
) y
dydx
c
( r
(
f
(
x
x
) y
(
, x
) y
dydx
) y
Page 12-2
,
y
))
,
A