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Definite integrals formulas
10 formulas for Definite integrals, from the Calculus section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Fundamental theorem | ∫ₐᵇ f(x) dx = F(b) − F(a) | |
| Reverse limits | ∫ₐᵇ f = −∫ᵇₐ f | |
| Splitting | ∫ₐᵇ f = ∫ₐᶜ f + ∫_cᵇ f | a < c < b |
| King property | ∫ₐᵇ f(x) dx = ∫ₐᵇ f(a + b − x) dx | |
| ∫₀ᵃ property | ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a − x) dx | |
| Even function | ∫₋ₐᵃ f = 2∫₀ᵃ f | |
| Odd function | ∫₋ₐᵃ f = 0 | |
| Periodic function | ∫₀ⁿᵀ f = n∫₀ᵀ f | |
| Wallis | ∫₀^(π/2) sinⁿx dx = (n−1)/n · (n−3)/(n−2) · … (× π/2 if n even) | |
| Leibniz rule | d/dx ∫_{a(x)}^{b(x)} f(t) dt = f(b)b′ − f(a)a′ |
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