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Mathematics Worksheet
📊 Definite Integrals
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Evaluate definite integrals using the Fundamental Theorem: F(b) − F(a).Interpret a definite integral as signed area.Handle intervals that cross the x-axis.Compute simple definite integrals accurately.📚 Quick Recap
A definite integral computes a specific numeric value — often representing the net area between a curve and the x-axis over a given interval.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1∫ from 0 to 2 of x3 dx = ?
2∫ from 1 to 4 of 3 dx = ?
3Fundamental Theorem: ∫ from a to b of f dx = ?
4∫ from −2 to 2 of x dx = ?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5FTC: ∫ from a to b of f(x) dx = .
6∫ from 0 to 2 of x3 dx = .
7Evaluate ∫ from 0 to 2 of x3 dx.
8Evaluate ∫ from 1 to 4 of 3 dx.
9Evaluate ∫ from 0 to 1 of (4x + 2) dx.
🚀 Section C · Challenge ● CHALLENGE 5
10Evaluate ∫ from −2 to 2 of x dx.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-B 2-B 3-A 4-A | 5 F(b) − F(a) 6 4 7 = 4 8 = 9 9 = 4 | 10 = 0