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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

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Calculus

Trapezoidal Rule Calculator

Approximate the definite integral of a function over [a, b] by summing trapezoid areas across n subintervals. Ideal for numerical integration when an antiderivative is difficult or impossible to find analytically.

Lower Limit (a)

Upper Limit (b)

Number of Subintervals

Average Trapezoid Height

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Key differences

	Area Under Curve Calculator	Trapezoidal Rule Calculator
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 the definite integral of a function over [a, b] by summing trapezoid areas across n subintervals. Ideal for numerical integration when an antiderivative is difficult or impossible to find analytically.