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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

Critical Points Calculator

Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero. Use it to locate the maximum or minimum of any parabola instantly.

x² Coefficient (a)

x Coefficient (b)

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Key differences

	Area Under Curve Calculator	Critical Points Calculator
Category	Calculus	Calculus
Inputs required	5	2
Result	Area Under Curve (square units)	Critical Point x-value
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.	Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero. Use it to locate the maximum or minimum of any parabola instantly.