BitWithBite
Mathematics Worksheet
🗂️ Multiple Integrals
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Evaluate double integrals over rectangular regions.Integrate one variable at a time as an iterated integral.Interpret a double integral as volume under a surface.Choose a convenient order of integration.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1∬ xy dA over [0,1]×[0,1] = ?
2∬ 3 dA over [0,4]×[0,2] = ?
3A double integral over a rectangle is evaluated as an ___ integral:
4∬ x2 dA over [0,2]×[0,3] = ?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5A double integral is evaluated as an integral.
6∬ xy dA over [0,1]×[0,1] = .
7Evaluate ∬ xy dA over [0,1]×[0,1].
8Evaluate ∬ 3 dA over [0,4]×[0,2].
9Evaluate ∬ x2 dA over [0,2]×[0,3].
🚀 Section C · Challenge ● CHALLENGE 5
10Evaluate ∬ (x + y) dA over [0,2]×[0,2].
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-C 2-C 3-B 4-B | 5 iterated 6 1/4 7 = 1/4 8 = 24 9 = 8 | 10 = 8