What is area between curves?
The region between two graphs over an interval, usually measured with absolute height |f−g|.
Area Between Two Curves Calculator
Find the signed or absolute area between two straight lines over an interval.
Enter two linear functions and bounds
f(x) = ax + b, g(x) = cx + d on [p, q].
About this calculator
How to use Area Between Two Curves Calculator, plus the formulas and logic behind the results.
Tool description
For lines, ∫(f−g) dx has a closed form. Absolute area accounts for crossings inside the interval.
How to use
- Enter coefficients for f and g.
- Enter interval endpoints p and q (p < q).
- Select Calculate.
- Review signed area and absolute area.
Formulas & reference
∫(f−g) dx = ∫((a−c)x + (b−d)) dxAntiderivative F(x) = ((a−c)/2)x² + (b−d)xSigned area = F(q) − F(p)
Interpretation
- Signed area can be negative
- Absolute area is always ≥ 0
- Crossing splits the integral
- Linear case is exact
Calculation logic
Computes the exact antiderivative difference. Absolute area splits at an interior intersection when the lines cross on (p,q).
Requires p < q. Parallel identical lines give zero area.
Area Between Two Curves Calculator FAQ
Common questions about this calculator and how to use the results.
Why signed and absolute?
Signed keeps orientation (f above/below g); absolute measures geometric area.
Do the lines need to intersect?
No. If they do not cross on [p,q], absolute area equals |signed area|.
What if p ≥ q?
The interval is invalid; enter p < q.
Are only lines supported?
This tool is specialized to linear f and g.
What if f = g?
Area is zero.