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 Top – Bottom method.

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

$\underset{a}{\overset{b}{\int }}f\left(x\right)\mathit{dx}\mathit{=}{F\left(x\right)|}_{x=a}^{x=b}\mathit{=}F\left(b\right)–F\left(a\right)$