The Two Main Antiderivative Rules
Special Case Antiderivatives (The ones you have to memorize)
U-Substitution
Initial Value Problems: Finding the +C
Fundamental Theorem of Calculus Part 1

Antiderivatives Overview

There are two main types of integrals, Definite Integrals and Indefinite Integrals. The Methods that you will use to find the antiderivatives will be the same. However, the final results will be different.

Definite Integral

Indefinite Integral

A Definite Integral is the exact net area between a curve, f ( x ) , and the x-axis .

It is the extension of a Riemann Sum which is an approximation of the net area between a curve, f ( x ) , and the x-axis .

An Indefinite Integral is giving you the general antiderivative of the equation. If you are starting with, f ( x ) , then the integral (antiderivative) would be how you get back the original f ( x ) .

Identifier:

Has an upper = b and lower = a bound on the integral.

Identifier:

Does not have an upper and lower bound on the integral.

a b f ( x ) dx

f ( x ) dx

Final Result:

 A Definite value, a number .

a b f ( x ) dx = F ( x ) | x = a x = b = F ( b ) F ( a )

 

Final Result

An Indefinite value, an equation .

f ( x ) dx = F ( x ) + C

OR

f ( x ) dx = f ( x ) + C

I like the second version, it reminds me that an antiderivative, undoes the derivative, f ( x ) , and the result is the original f ( x ) .

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