Chapter 5: Double Integration
Section 5.5: Numeric Evaluation of Iterated Integrals
Example 5.5.1
Evaluate ∫03∫y1/32ⅇx− yx2+coshy ⅆx ⅆy numerically.
Solution
Maple Solution - Interactive
Control-drag the given iterated integral, making sure to change to Maple's exponential "e".
Context Panel: 2-D Math≻Convert To≻Inert Form
Context Panel: Approximate≻10 (digits)
∫03∫y1/32ⅇx− yx2+coshy ⅆx ⅆy→at 10 digits1.348520251
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≔Intⅇx− yx2+coshy,x=y1/3..2,y=0..3:
Apply the evalf command to launch a numeric evaluation of the integral.
evalfq = 1.348520251
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