Integrate Dy/dx Calculator

What is dy/dx?

In calculus, dy/dx represents the derivative of y with respect to x. It measures how a function y changes as its input x changes. The integral of dy/dx, written as ∫dy/dx, is the antiderivative that reconstructs the original function y.

Understanding dy/dx is fundamental to solving problems in physics, engineering, economics, and many other fields where rates of change are important.

How to Integrate dy/dx

Integrating dy/dx involves finding the antiderivative of the derivative function. The process follows these general steps:

1. Identify the derivative function dy/dx.
2. Find its antiderivative, which is the integral ∫dy/dx.
3. Add a constant of integration (C) to represent the family of possible solutions.
4. Apply initial conditions if specific values are known.

This process essentially reverses differentiation, helping you recover the original function from its rate of change.

Formula

This formula shows that integrating a derivative function returns the original function plus an arbitrary constant.

Example Calculation

Let's find the integral of the derivative function dy/dx = 3x².

1. Identify the derivative: dy/dx = 3x².
2. Find the antiderivative: ∫3x² dx = x³ + C.
3. Add the constant of integration: x³ + C.

The result is x³ + C, which is the original function before differentiation.