Compare calculators

Both calculators run independently — change the inputs on either side to compare results.

Area Under Curve Calculator

Computes the exact area between a parabola f(x) = ax² + bx + c and the x-axis over an interval [x₁, x₂]. Use it to evaluate definite integrals for quadratic functions in physics, economics, or calculus coursework.

Coefficient of x²

Coefficient of x

Constant Term

Starting x-value

Ending x-value

Fill in the required fields to see your result.

Calculus

Rectangular Rule Integration

Approximate a definite integral using a rectangular (midpoint-style) rule with a chosen number of subintervals and an averaged function value. Returns the area of a single representative rectangle of width Δx.

Lower Bound (a)

Upper Bound (b)

Number of Intervals (n)

Average Function Value

Fill in the required fields to see your result.

Key differences

	Area Under Curve Calculator	Rectangular Rule Integration
Category	Calculus	Calculus
Inputs required	5	4
Result	Area Under Curve (square units)	Approximate Integral
What it does	Computes the exact area between a parabola f(x) = ax² + bx + c and the x-axis over an interval [x₁, x₂]. Use it to evaluate definite integrals for quadratic functions in physics, economics, or calculus coursework.	Approximate a definite integral using a rectangular (midpoint-style) rule with a chosen number of subintervals and an averaged function value. Returns the area of a single representative rectangle of width Δx.