Chapter 5: Double Integration
Section 5.5: Numeric Evaluation of Iterated Integrals
Evaluate ∫−13∫x22 x+3coshx cosy ⅆy ⅆx numerically.
Maple Solution - Interactive
Control-drag the given iterated integral.
Context Panel: 2-D Math≻Convert To≻Inert Form
Context Panel: Approximate≻10 (digits)
∫−13∫x22 x+3coshx cosy ⅆy ⅆx→at 10 digits16.47752898
While this recipe used to work in Maple, by the time it was checked in Maple 2020, it was discovered to fail. Surprisingly, if this worksheet is executed with the triple exclamation in the toolbar, the numeric integration succeeds, even though the option "Approximate" does not appear in the Context Panel!
The alternative seems to be this: To the inert form of the integral, apply the Context Panel option "Apply a Command" and fill in the first line of the resulting dialog with evalf. (This is essentially what the Coded Solution does.) The second line of the "Apply a Command" dialog can be used to specify the number of digits to be used in the numeric evaluation of the integral. The default number is 10.
∫−13∫x22 x+3coshx cosy ⅆy ⅆx→16.47752898
The ordinary advice given for the numeric evaluation of an integral is in the folowing paragraph. That this does not seem to work for iterated integrals would be, in this author's opinion, a regression in Maple that is yet to be fixed.
If the iterated integral is not first converted to its inert form, Maple will immediately seek an exact evaluation of the integral. When it discovers that it cannot find the appropriate antiderivative(s), it then switches to numeric mode. Since it can take Maple quite some time before it gives up on the search for an exact value, if the user knows in advance that a numeric evaluation is called for, it should be initiated immediately by first converting the integral to inert form.
Maple Solution - Coded
Use the Int command to form the unevaluated (inert) integral.
q≔Intcoshx cosy,y=x2..2 x+3,x=−1..3:
Apply the evalf command to launch a numeric evaluation of the integral.
evalfq = 16.47752898
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