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Mathematics Worksheet
📈 Area Under Curve
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Compute the area under a curve using a definite integral.Find the area between two curves.Choose correct limits and identify the top function.Interpret area as an accumulated quantity.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1Area under f(x) = x2 from 0 to 4 = ?
2Area under f(x) = 3x from 0 to 2 = ?
3Area between two curves = ?
4Area under f(x) = x3 from 0 to 2 = ?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Area under a curve is computed with a integral.
6Area between curves = ∫( − bottom) dx.
7Find the area under f(x) = x2 from x = 0 to x = 4.
8Find the area under f(x) = 3x from x = 0 to x = 2.
9Find the area between f(x) = x + 3 and g(x) = x2 from x = −1 to x = 2.
🚀 Section C · Challenge ● CHALLENGE 5
10Find the area under f(x) = x3 from x = 0 to x = 2.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-B 2-B 3-A 4-B | 5 definite 6 top 7 = 64/3 8 = 6 9 = 9/2 | 10 = 4