Practice question · Multiple choice
Fubini's theorem lets you swap the order of integration over a rectangle. Why is that practically valuable rather than merely elegant?
Hints
- Ask what changes when you integrate with respect to y first rather than x.
- The answer is the same either way. What differs?
Show the answer
B. Because one order can be elementary and the other intractable
Why
Both orders give the same number and one may be far easier to reach, the classic case being integrals with no elementary antiderivative in one variable and a trivial one in the other. Option 4 gets it backwards: equality of the two orders is precisely what the theorem asserts.
Practise Multiple Integration
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More questions on Multiple Integration
- Fubini's theorem lets you swap the order of integration for any bounded function.
- Estimate ∫ 0⁴ (8 - 2x) dx, the area of the triangle with base 4 and height 8.
- Match each integration concept to its meaning.
- Sort these into single integrals vs double integrals.
- Over the rectangle [0,3]×[0,2] the two orders of integration have the same limits; over a triangle they do…