Filter
Top Products
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
)),(( yxf
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<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
∫∫∫∫∫∫
==
d
c
ys
yr
b
a
xg
xf
R
dydxyxdydxyxdAyx
)(
)(
)(
)(
),(),(),( φφφ
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.