HP 50g HP 50g_user's manual_English_HDPSG49AEM8.pdf - Page 141
Multiple integrals, Reference
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To define the functions f(x,y) and g(x,y,z), in ALG mode, use: DEF(f(x,y)=x*COS(y)) ` DEF(g(x,y,z)=√(x^2+y^2)*SIN(z) ` To type the derivative symbol use ,¿. The derivative ∂ ( f (x, y)) , ∂x 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
Page 12-2
To define the functions f(x,y) and g(x,y,z), in ALG mode, use:
DEF(f(x,y)=x*COS(y))
`
DEF(g(x,y,z)=
√
(x^2+y^2)*SIN(z)
`
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
Calculating a double integral in the calculator is straightforward.
A
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.
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