Calculatrice d'Aire sous la CourbeFormule

Area Under a Curve

Definite Integral

The area under y = ax^n from x₁ to x₂ is:

Area = integral from x₁ to x₂ of ax^n dx

=(a/(n+1)) × [x₂^(n+1) - x₁^(n+1)]

Average Value

The average value of f on [x₁, x₂] is:

f_avg = (1/(x₂ - x₁)) × integral of f(x) dx

Exemple Résolu

Find the area under y = x² from x = 0 to x = 4.

  1. Antiderivative: x³/3
  2. F(4) = 64/3 ≈ 21.3333
  3. F(0) = 0
  4. Area = 21.3333 - 0 = 21.3333
  5. Average value = 21.3333 / 4 ≈ 5.3333