Practice question · Match the pairs
Match each integration concept to its meaning.
- Iterated integral
- Fubini's theorem
- Jacobian
- Consumer surplus
- Area between demand curve and market price
- Evaluate a double integral as two nested single integrals
- Order of integration can be switched for continuous functions
- Scaling factor for a change of variables in multiple integrals
Hints
- Separate the computation method from the theorem that permits swapping.
- One factor corrects for a change of coordinates.
Show the answer
- Iterated integral → Evaluate a double integral as two nested single integrals
- Fubini's theorem → Order of integration can be switched for continuous functions
- Jacobian → Scaling factor for a change of variables in multiple integrals
- Consumer surplus → Area between demand curve and market price
Why
Iterated integrals compute the double integral; Fubini lets you swap order; the Jacobian handles coordinate changes; surplus is the economic payoff.
Practise Multiple Integration
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