What this page does
You type the coefficients of a polynomial up to x⁴, and the page differentiates and integrates it symbolically rather than numerically.
For x² − 3x + 1 the derivative is 2x − 3, the second derivative is 2, and the antiderivative is x³/3 − 3x²/2 + x + C.
Worked example
Take f(x) = x² − 3x + 1, evaluate at x = 2, and integrate from −1 to 3.
At x = 2 the value is −1 and the gradient is 1. The definite integral over that range is 1.333333, and the average value is 0.333333.
Stationary points
A stationary point is where the gradient is zero, so it is a root of the derivative. For this curve that is x = 1.5, where y = −1.25.
The calculator finds them numerically across −20 to 20, which covers every cubic and quartic you are likely to enter.
What it does not do
It handles polynomials only. Derivatives of sin, cos, ln or exponentials need a computer algebra system, which this page does not have.
If you need those, the graphing page will plot them, and the numeric check will confirm an integral to nine decimal places.
Inputs for the calculus calculator
Coefficients
One box per power, from x⁴ down to the constant. Leave a power at 0 if it is missing.
Evaluate at x =
The point where the value and the gradient are reported.
Range
The two ends used for the definite integral and the plot.
CALCULATOR QUESTIONS
Calculus calculator questions
How do I differentiate x² − 3x + 1?
Bring each power down and reduce it by one: 2x − 3. The constant term disappears.
What is the integral of x² − 3x + 1?
x³/3 − 3x²/2 + x + C. Each power goes up by one and is divided by the new power.
Can it differentiate sin(x) or ln(x)?
No. This page works with polynomials. For other functions the graphing page will still plot them.
What is the average value of a function?
The definite integral divided by the width of the range, which is the height of the rectangle with the same area.