Chapter 5: Double Integration
Section 5.4: Changing the Order of Iteration
Example 5.4.4
Evaluate , reverse the order of integration, and evaluate again.
Solution
Mathematical Solution
Figure 5.4.4(a) Integration in the order
Figure 5.4.4(b) Integration in the order
Maple Solution - Interactive
Evaluate the given integral
Control-drag the given integral. Context Panel: Evaluate and Display Inline
=
Use the visualization task template in Table 5.4.4(a) to obtain the value of the integral and a graph of the region of integration.
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Visualizing Regions of Integration≻
Evaluate and Graph
Area Element
Select dAdy dxdx dy
,
Value of Integral
Bounding Curves
"Volume"
Table 5.4.4(a) Integration in the order
Guided by Table 5.4.4(a), reverse the order of integration
Calculus palette: Iterated double-integral template.
Context Panel: Evaluate and Display Inline
Maple Solution - Coded
Apply the int command.
Graph the region of integration
Apply the inequal command from the plots package to graph the feasible region common to a set of inequalities.
Each of the four limits in the iterated integral must be expressed as a separate inequality.
Reverse the order of integration
Apply the Int command, using the graph of the region of integration as a guide.
Evaluate the inert integral with the value command.
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