HP 48gII dydx, @EVAL, Reference, Multiple integrals, ∫∫φ (x, y)dA = ∫ab∫fg((xx))φ (x, y)dydx = ∫cd ∫rs((yy))φ (x, y)dydx

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

∫∫φ (x, y)dA = ∫ab∫fg((xx))φ (x, y)dydx = ∫cd ∫rs((yy))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), 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 guide.

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