Definite Integrals

Grade 12 Maths — Definite Integrals: 25 practice questions with instant scoring and explanations.

1. The Fundamental Theorem of Calculus states:
2. ∫[0,1] x² dx equals:
3. ∫[0,π] sin(x) dx equals:
4. ∫[1,e] (1/x) dx equals:
5. ∫[a,b] f(x) dx = −∫[b,a] f(x) dx is:
6. ∫[a,a] f(x) dx equals:
7. ∫[0,2] (3x + 1) dx equals:
8. For a ≤ c ≤ b: ∫[a,b] f(x) dx = ∫[a,c] f(x) dx + ∫[c,b] f(x) dx is:
9. ∫[−1,1] x³ dx equals:
10. If f is odd, then ∫[−a,a] f(x) dx equals:
11. If f is even, then ∫[−a,a] f(x) dx equals:
12. ∫[0,π/2] cos(x) dx equals:
13. ∫[1,2] e^x dx equals:
14. ∫[0,1] (1 + 2x + 3x²) dx equals:
15. ∫[−2,2] |x| dx equals:
16. The Mean Value Theorem for Integrals states that there exists c ∈ [a,b] such that:
17. ∫[0,4] √x dx equals:
18. ∫[−π/2,π/2] sin(x) dx equals:
19. If ∫[a,b] f(x) dx ≥ 0, then:
20. ∫[0,1] (e^x − 1) dx equals:
21. For continuous f: d/dx[∫[a,x] f(t) dt] equals:
22. ∫[0,π] sin²(x) dx equals:
23. Question?
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25. Question?