Practice question · Sort into groups
Sort these into single integrals vs double integrals.
Groups: Single integral · Double integral
- Joint surplus over a two-good region
- Consumer surplus triangle
- Area under a curve
- Volume under a surface
Hints
- Count how many variables are being integrated over.
- One integral sign per dimension.
Show the answer
Single integral: , Area under a curve, Consumer surplus triangle
Double integral: , Volume under a surface, Joint surplus over a two-good region
Why
Single integrals compute areas; double integrals compute volumes or areas in higher-dimensional settings.
Practise Multiple Integration
The app has 7 more questions on this lesson, and keeps your place in the course. Business I is free to start.
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.
- Fubini's theorem lets you swap the order of integration over a rectangle. Why is that practically valuable…
- Over the rectangle [0,3]×[0,2] the two orders of integration have the same limits; over a triangle they do…