How to use the Integral Calculator

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. 
See a stepbystep solution
If you need to understand how the problem was solved, you can see a detailed stepbystep solution. 
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 antiderivatives, the area of twodimensional regions, volumes, central points, among many other ways. Knowing how to use integration rules is, therefore, key to being good at Calculus.
But, let’s start with the basics; Integrals. What is Integrals?
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 antiderivative 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 xaxis 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.