# Integral Calculator

## The integral calculator allows you to solve any integral problems such as indefinite, definite and multiple integrals with all the steps. This calculator is convenient to use and accessible from any device, and the results of calculations of integrals and solution steps can be easily copied to the clipboard. Solve integrals with incredible ease!

Add to Bookmarks Press Ctrl+D (for Windows / Linux) or Cmd+D (for MacOS)

## How to use the Integral Calculator

1. ### Type in the integral problem to solve

To get started, type in a value of the integral problem and click «Submit» button. In a moment you will receive the calculation result.
2. ### See a step-by-step solution

If you need to understand how the problem was solved, you can see a detailed step-by-step solution.
3. ### Save the results of your calculation

After finishing, you can copy the calculation result to the clipboard, or enter a new problem to solve.

## What is Integrals?

One of the essential tools in Calculus is Integration. We use it to find anti-derivatives, the area of two-dimensional regions, volumes, central points, among many other ways. Knowing how to use integration rules is, therefore, key to being good at Calculus.

There are two types of integrals: The indefinite integral and the definite integral. The indefinite integral f(x), which is denoted by f(x) dx, is the anti-derivative of f(x). The derivative of f(x) dx is, therefore, f(x). As you might already be aware, the derivative of a constant is always 0. For this reason, indefinite integrals are only defined up to some arbitrary constant. Consider sin(x)dx = -cos (x) + constant. The derivative of –cos(x) + constant is sin (x).

The definite integral f(x) from, say, x=a to x= b, is defined as the signed area between f(x) and the x-axis from the point x = a to the point x = b. The definite integral is denoted by a f(x) d(x).

It is important to note that both the definite and indefinite integrals are interlinked by the fundamental theorem of calculus. The theorem states that if f(x) is continuous on [a,b], and F(x) is its continuous indefinate integral, then a f(x) dx= F(b) – F(a). This, therefore, means that 0 sin(x) dx = {-cos(π)} – {-cos(0)} = 2.

Note, however, that sometimes, you may be required to find an approximation to a definite integral. The most common way to do this is to have several thin rectangles under the curve from the initial point x = a to the last point x = b. Add the signed areas (areas of the rectangles) together, and there you go! You have the desired definite integral. 