How to use the definite integral of a quadratic calculator
Find the exact area under a quadratic curve between two x values. Enter coefficient a, coefficient b, constant c, lower limit, upper limit in the fields above; the definite integral is computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “area under parabola”, “definite integral quadratic”, “integral of ax² + bx + c”, “calculate definite integral of a quadratic”, “find definite integral”.
Formula
Variables
- a — Coefficient a
- b — Coefficient b
- c — Constant c
- x1 — Lower limit
- x2 — Upper limit
Worked example
With coefficient a = 1, coefficient b = 0, constant c = 2, lower limit = 0, upper limit = 3, the calculator gives definite integral ≈ 15.
Frequently asked questions
What is the definite integral of a quadratic calculator used for?
Find the exact area under a quadratic curve between two x values. It helps with questions such as “area under parabola”, “definite integral quadratic”, “integral of ax² + bx + c”.
What is the formula for the definite integral of a quadratic calculation?
Definite integral = a × (x2^3-x1^3) / 3+b × (x2 × x2-x1 × x1) / 2+c × (x2-x1). Here a is coefficient a, b is coefficient b, c is constant c, x1 is lower limit, x2 is upper limit.
What inputs do I need for the definite integral of a quadratic calculator?
You need coefficient a, coefficient b, constant c, lower limit, upper limit. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the definite integral of a quadratic calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the definite integral of a quadratic result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.