Area between a curve and a line (Edexcel A-Level Mathematics): Flashcards

Integrate the top curve, subtract the bottom curve's integral.

Find points of intersection by solving $f(x) = g(x)$.

Integrate the absolute difference over the interval $[a, b]$.

Split the integral at the crossing point(s).

Area = $\int_{a}^{b} (f(x) - g(x)) dx$.

Area = $\int_{a}^{b} (g(x) - f(x)) dx$, if $g(x) > f(x)$.

Set equations equal, integrate, and find area: $4$ units.

Compute the antiderivative from $a$ to $b$, then simplify.

Check units and if the result makes sense in context.

Find intersections, set up integral, compute the area.