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Area Between Curves Calculator

Find the exact area enclosed between any two functions

The area between two curves f(x) and g(x) over an interval [a, b] is:

A = \int_a^b |f(x) - g(x)|\, dx

When the curves form a closed region (they intersect at two or more points), the area is automatically computed between the intersection points — no need to specify bounds.

This area between curves calculator with graph shows the region visually on an interactive graph — see the curves, their intersection points, and the shaded enclosed area in real time. Type two functions, and the AI finds their intersections, computes the exact area, and highlights it on the graph. Zoom and pan to explore. Works with polynomials, trigonometric, exponential — any pair of functions.

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FAQ

How do I find the area between two curves?
Step 1: Find where the curves intersect (set f(x) = g(x)). Step 2: Integrate |f(x) − g(x)| between the intersection points. This calculator does both steps automatically — just give it two functions.
What if the curves cross multiple times?
The calculator finds all intersection points and computes the area of each enclosed region separately, then gives you the total. Each region is listed with its bounds and area.
What does it mean when the area is "divergent"?
If two curves intersect only once (or never), they diverge to infinity in at least one direction. The enclosed area is infinite — there is no finite "area between" them. The calculator detects this and tells you.
Can I specify a range instead of using intersections?
Yes. Say "area between x^2 and 2x from 0 to 3" and the calculator integrates over exactly that interval. Without bounds, it automatically uses the intersection points.
Does this work with trigonometric functions?
Yes. For example, the area between sin(x) and cos(x) from 0 to 2π consists of multiple enclosed regions. The calculator finds all intersections and computes each region.
Why use an area between curves calculator with a graph?
The graph shows you exactly which region is being measured — you can see the two curves, their intersection points, and the enclosed area visually. This makes it much easier to understand what the integral represents and catch errors. You can also zoom in to see how the curves cross and where the area is concentrated.

Related Topics

Integrals (lesson)Function Intersection CalculatorTangent Line Calculator