Definite Integrals & Properties

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

1. Definite integral ∫_a^b f(x)dx represents:
2. Fundamental Theorem of Calculus: ∫_a^b f(x)dx =
3. ∫_a^a f(x)dx =
4. ∫_a^b f(x)dx + ∫_b^c f(x)dx =
5. ∫_a^b f(x)dx = -∫_b^a f(x)dx is:
6. ∫_a^b k·f(x)dx = (k is constant)
7. ∫_a^b (f(x) + g(x))dx =
8. If f(x) ≥ 0 on [a,b], then ∫_a^b f(x)dx:
9. If f(x) ≥ g(x) on [a,b], then:
10. Mean Value Theorem for Integrals: ∫_a^b f(x)dx =
11. ∫_0^π sin(x)dx =
12. ∫_0^π cos(x)dx =
13. ∫_0^1 x^n dx =
14. ∫_0^∞ e^(-x)dx =
15. If f is even, ∫_(-a)^a f(x)dx =
16. If f is odd, ∫_(-a)^a f(x)dx =
17. ∫_1^e ln(x)dx =
18. Cauchy-Schwarz inequality for integrals: (∫f·g)² ≤
19. For substitution in definite integrals ∫_a^b f(g(x))g'(x)dx with u = g(x):
20. ∫_0^(π/2) sin²(x)dx =
21. ∫_0^(π/2) cos²(x)dx =
22. Wallis formula ∫_0^(π/2) sin^n(x)dx uses:
23. Leibniz rule for differentiating under integral sign d/da[∫_a^b f(x,a)dx] =
24. For improper integrals ∫_a^∞ f(x)dx, we evaluate as:
25. Review question for Definite Integrals & Properties