Mastering Integral Calculus
Integration is the reverse operation of differentiation (antiderivative). It is used to calculate net accumulation, totals, and areas under curves.
Essential Integration Formulas
- Power Rule: ∫ xⁿ dx = (xⁿ⁺¹ / (n + 1)) + C
- Exponential Rule: ∫ eᵏˣ dx = (1/k) · eᵏˣ + C
- Trig Integrals: ∫ sin(x) dx = −cos(x) + C | ∫ cos(x) dx = sin(x) + C
- Integration by Parts: ∫ u dv = u·v − ∫ v du
- U-Substitution: Set u = g(x), du = g'(x)dx to simplify complex composite integrals.