HP 49g manual Multiple integrals, Φ x, ydydx

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)) , for

∂x

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

b g ( x)	d	s( y )
∫∫φ( x, y)dA = ∫ a ∫ f ( x) φ ( x, y)dydx = ∫ c		∫r ( y ) φ( x, y)dydx

R

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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