Practice question · Multiple choice
Swapping the order of integration in a double integral often makes it far easier. Why can the two integrals not simply share the same limits?
Hints
- Sketch the region and slice it the other way.
- Ask what the inner limits depend on in each order.
Show the answer
B. The LIMITS, since they describe the region by the outer variable
Why
The region is the same; its description is not. Sketching it is the reliable way to get the new limits, and Fubini guarantees the answers agree once they are right.
Practise Double Integrals
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More questions on Double Integrals
- Rain falls with varying intensity r(x,y) over a city. What does ∬ city r(x,y) dA compute?
- A rectangular plate 0 ≤ x ≤ 3, 0 ≤ y ≤ 2 has uniform density 5 kg/m². Using ∬ 5 dA, find its mass in kg.
- Order the steps for evaluating ∬ R xy dA over a triangle by iterated integration.
- Sort each application into what a double integral computes.