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

Method: Antiderivative of Constants

Step 1: Simplify and look for algebraic rewrites.

This is your new version of Option 1 from limits. This means it is the first thing you will always want to do before you start actually applying a derivative rule. You must ensure that the equation is ready to have a derivative taken.

  • Roots or Radicals
  • x’s on the bottom of a fraction.
  • Trig functions raised to a power.

Step 2: Identify any term(s) that are just a constant.

Step 3: Take the antiderivativeof the constant using the Recipe: Numbers by themselves, constants, gain a letter back.

This means just adding a letter back to it the constant. Remember you are undoing a derivative.

Step 4 ( Definite Integral ONLY ): Evaluate the antiderivative result using the TopBottom method.

Plug the upper bound into your antiderivative and subtract off the lower bound plugged into your antiderivative.

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

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