# Integrating dx and dy: What Does It Mean?

• Blue and green
In summary, dx and dy are used to indicate the variable that is being integrated in terms of. After integration, there should no longer be any "dx" or "dy" in the expression. These symbols represent infinitesimal units of length along the x and y axes respectively, and can be used to create more complex shapes when integrated together.
Blue and green
Once you've integrated, dx and dy just indicate what variable you've integrated in terms of, correct?

Yeah. In response to the question in the title, dx does mean something.

One of the things that people associate with dx is an infinitesimal unit of length along the x axis.

"Once you've integrated"- that is after you have done the integration- there should no longer be a "dx" or "dy" in the expression!

As mentioned above dx just means "a little piece of x". So A dx is just the A times a little piece dx. Integrating means you do this many times, and add up the results. You can even do dx dy to have little squares, and other such things if you get clever!

davidbenari

## 1. What is the difference between dx and dy in calculus?

The notation dx and dy are used to represent infinitesimal changes in the independent variable x and dependent variable y, respectively. In calculus, dx represents the change in x and dy represents the change in y as the independent variable changes.

## 2. How do you integrate using dx and dy?

The process of integrating using dx and dy involves finding the antiderivative of the function with respect to the independent variable x. The notation for the integral using dx is ∫ f(x) dx, which means the integral of the function f(x) with respect to x. Similarly, the notation for the integral using dy is ∫ f(y) dy, which means the integral of the function f(y) with respect to y.

## 3. What is the meaning of integrating dx and dy in terms of area?

Integrating using dx and dy can be thought of as finding the area under a curve. The integral of a function f(x) with respect to x is the sum of all the small areas under the curve, with the width of each strip being dx. Similarly, the integral of a function f(y) with respect to y is the sum of all the small areas under the curve, with the width of each strip being dy.

## 4. Can dx and dy be used interchangeably in integration?

No, dx and dy cannot be used interchangeably in integration. They represent infinitesimal changes in different variables and have different meanings. The notation used should correspond to the independent variable being considered in the integral.

## 5. How do you solve integrals using dx and dy in multivariable calculus?

In multivariable calculus, integrating using dx and dy involves finding the antiderivative of a function with respect to multiple variables. This is done by integrating one variable at a time, while treating the other variables as constants. The notation used for this type of integration is ∫∫ f(x,y) dx dy, which means the integral of the function f(x,y) with respect to both x and y.

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