Integrals

The re-construction of a function from its derivative is anti-differentiation integration OR

So…

Find the anti-derivative of 3x 2

Power Rule for Derivatives 1. Multiply by the exponent 2. Subtract 1 from exponent Anti-derivative is opposite Divide Add 1. 2.

Power Rule for Integrals 1. Add 1 to the exponent 2. Divide by the exponent

Power Rule for Integrals 1. Add 1 to the exponent 2. Divide by the exponent

Power Rule for Anti-Derivatives 1. Add 1 to the exponent 2. Divide by the exponent

Anti-Derivatives from Definitions Since then Since then

Properties of integrals Like with derivatives

Properties of integrals Like with derivatives

Properties of integrals

Since we are given the derivative of cost, we need to do the anti-derivative to find cost.