Calculus Calculator

What is Calculus?

Calculus is the mathematical study of continuous change. It has two major branches, both of which you can calculate here:

1. Differential Calculus (Derivative)

This measures the Rate of Change. If you have a function that represents the position of a car, the derivative tells you its speed (velocity) at any exact moment.
Geometrically, the derivative at a point is the Slope of the Tangent Line touching the curve at that point.

2. Integral Calculus (Integral)

This measures Accumulation or Area. If you have a function representing the speed of a car, the integral tells you the total distance traveled over a time period.
Geometrically, the definite integral is the Area Under the Curve between two points on the x-axis.

How This Calculator Works

This tool uses Numerical Methods to solve calculus problems instantly without complex symbolic algebra.

For Derivatives (Slope):

It uses the Central Difference Method. To find the slope at `x`, it calculates the value of the function slightly ahead `(x+h)` and slightly behind `(x-h)`, then finds the slope between them.
f'(x) ≈ [f(x+h) - f(x-h)] / 2h (where h is a tiny number)

For Integrals (Area):

It uses the Trapezoidal Rule (a form of Riemann Sums). It slices the area under the curve into hundreds of tiny trapezoids, calculates the area of each, and sums them up to give you a precise result.

Syntax Guide

To ensure accurate results, type your functions like this:

• Multiplication: Use * (e.g., 2*x not 2x).
• Powers: Use ^ (e.g., x^2, x^3).
• Trig Functions: sin(x), cos(x), tan(x).
• Exponentials: e^x or exp(x).
• Logarithms: log(x) (base 10) or ln(x) (natural log).