Lesson 8 of 18Article20 min
Integrals as Antiderivatives
An antiderivative of f is any F with F′ = f. The indefinite integral ∫ f(x) dx names the whole family F(x) + C.
Reversing differentiation
An antiderivative of f is any F with F′ = f. The indefinite integral ∫ f(x) dx names the whole family F(x) + C.
Must-know antiderivatives
Always write + C for indefinite integrals unless an initial condition pins C down.
Worked example with initial condition
f′(x) = 6x and f(1) = 4. Then f(x) = 3x² + C. Using f(1)=4: 3+C=4 → C=1 → f(x)=3x²+1.