Indefinite integration
Integration as differentiation in reverse: integrating powers of , why there is always a , and how one point pins down the exact curve.
≈ 40 minIntegrating powers of x
Integration undoes differentiation: raise the power by one and divide by the new power, then add because any constant would have vanished when differentiating. As with differentiation, rewrite roots, fractions and brackets as separate powers of first.
≈ 30 minFinding a curve from its gradient
Integrating a gradient function gives a whole family of curves, . One known point picks out the single curve you want: substitute the point and solve for .
≈ 30 min