Question 1

What is an Antiderivative?

Accepted Answer

In calculus, an antiderivative (or indefinite integral) of a function f(x) is a new function F(x) whose derivative is equal to the original function f(x). It is essentially the reverse process of taking a derivative.

Question 2

Why is there always a '+ C' at the end?

Accepted Answer

The '+ C' represents the Constant of Integration. Because the derivative of any constant number (like 5, 12, or -100) is zero, when you take an antiderivative, you don't know if the original function had a constant attached to it. Adding '+ C' acknowledges that there is an entire family of functions that share the same derivative.

Question 3

What is the Power Rule for Integration?

Accepted Answer

The most common rule for finding antiderivatives of polynomials is the Power Rule: to integrate x^n, you increase the exponent by 1 (n+1) and then divide the entire term by that new exponent. For example, the antiderivative of x^2 becomes (x^3)/3.

Question 4

What is the difference between an Indefinite and Definite Integral?

Accepted Answer

An indefinite integral (antiderivative) results in a function containing variables (like F(x) + C). A definite integral evaluates the antiderivative between two specific limits (bounds 'a' and 'b'), resulting in a single numerical value representing the total area under the curve between those two points.

Question 5

Why do some functions not have an antiderivative?

Accepted Answer

Most elementary functions have an antiderivative, but some visually simple functions (like e^(-x^2) or sin(x)/x) do not have antiderivatives that can be expressed using elementary functions (standard algebra, trig, and exponentials). These require completely different mathematical techniques to evaluate bounded areas.

Antiderivative Calculator

Common Antiderivative Rules

Frequently Asked Questions

Share With Your Study Group

Related Calculators