Antiderivatives of Constants & Power Functions

Instructor: David Karsner
In the study of calculus, you are frequently called on to find the antiderivative of a function. In this lesson, you'll learn how to find antiderivatives of constants and power functions.

What Is an Antiderivative?

Imagine you are hiking through the woods and come across an animal track left in the mud. Can you determine what animal created that track? This process of working backwards to find out what created the animal track is similar to the the process of working backwards to find the antiderivative of a function.

In calculus, you have to find the derivative of many different types of functions. The derivative is the rate of change of a function at a given point, x. For example, the derivative of f(x)=x2-4x+2 would be 2x-4.

Finding the antiderivative involves starting with a function and then finding what other function would have created the first function by taking the derivative. If the function was f(x)=2x-4, an antiderivative would be F(x)=x2-4x+2. The antiderivative and the integral have similar definitions. A definite integral, which is the area under a curve from point a to b, is a value, and the antiderivative is a function. The indefinite integral and the antiderivative are even closer in definition, and for the purpose of this lesson, can be used as synonyms. Derivatives are denoted with f(x), whereas the antiderivative of f(x) is denoted with a capital letter F(x).

The Antiderivative of a Power Function

Power functions have the form of f(x)=axb. They have one term in which you have a constant (a) times a variable x raised to some power. Examples of power functions would f(x)=3x2 and g(x)=.5x5. To find the antiderivative of a power function follow these steps.

  1. Notice the exponent and add one.
  2. Divide the term by the exponent plus one.
  3. The result of the second step plus a constant C will be the antiderivative.

The antiderivative will have the +C at the end of it. You'll learn more about this later in the lesson. The antiderivative of a power function will always have a degree, the largest exponent in the function, that is one greater than the original function.

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support