Area Under Curves
Recover a function from its derivative, then find areas using definite integration.
Reverse differentiation
Positive area / derivative
Negative area
Your function
Integration dashboard
Signed area0
Total area0
Adjust your controls to update both plots.
The maths
Reverse differentiation: if f′(x) = 2Ax + B, then f(x) = Ax² + Bx + C. Use a given point to determine C.
Definite integral: ∫ₐᵇ f(x) dx = F(b) − F(a), where F′(x) = f(x).
The definite integral gives signed area. For geometric area, split at each x-intercept and add the absolute areas. Areas are measured in units².
One thin strip
Area of a narrow strip ≈ height × width.