Integrals & FTC Tutor Help
Undo the derivative: antiderivatives rebuild a function from its rate of change. The Fundamental Theorem of Calculus turns area problems into antiderivative evaluations — with net area keeping honest count below the axis.
1 Concept recap
The essentials of Antiderivatives & the Definite Integral (FTC), on one screen.
Antiderivative
F with F′ = f. Power rule: ∫ xn dx = xn+1/(n+1) + C (n ≠ −1). Always end with + C.
FTC
∫ab f(x) dx = F(b) − F(a). Differentiation and integration undo each other.
Net area
Above the x-axis counts positive, below counts negative. Total area needs |f| or splitting at zeros.
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