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Introduction to integration and area
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Learn it Integration reverses differentiation: ∫xⁿ dx = xⁿ⁺¹/(n + 1) + C (n ≠ −1). A definite integral ∫ₐᵇ f(x) dx = F(b) − F(a) gives the area under the curve (above the x-axis). The trapezoidal rule estimates area from data.
Example: Area under y = 3x² from x = 0 to 2?
- ∫ 3x² dx = x³.
- 2³ − 0³ = 8.
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