Area Under the Curve Calculator

The Area Under the Curve Calculator determines the area associated with a function over a chosen interval. For a continuous function, a definite integral gives the signed area between the graph and the x-axis. Use the tool to work through the calculation and review the result.

Definite
Indefinite

with respect to

Upper Limit: (inf = ∞ , pi = π)

Lower Limit: (inf = ∞ , pi = π)

Integral used for area

For f(x) from x = a to x = b, the signed area is ∫ₐᵇ f(x) dx. Regions below the x-axis contribute negative values. If you need total geometric area, those regions must be treated separately or the absolute value of the function must be integrated.

Worked example

For f(x) = x from 0 to 2, the integral is ∫₀² x dx = [x²/2]₀² = 2. The graph forms a triangle with base 2 and height 2, whose geometric area is also 2 square units.

Using the calculator

Enter the function.
Set the lower and upper limits.
Calculate the definite integral.
Check whether the interval contains portions below the x-axis.

Frequently Asked Questions FAQ

Does a definite integral always equal geometric area?

Not always. A definite integral gives signed area, so portions below the x-axis contribute negative values.

What is the area under y=x from 0 to 2?

The integral is ∫₀²x dx=2, which also matches the triangle area with base 2 and height 2.

When should an interval be split?

If the function crosses the x-axis and total geometric area is required, split the interval at the crossing points so negative and positive regions can be handled separately.

Have Feedback or a Suggestion?

Kindy let us know your reveiws about this page

;