**Antiderivative (Indefinite Integral):**

The opposite of the derivative, so what function leads to the derivative.

Actually, a “set” of functions, as there is an infinite amount of antiderivative functions b/c “+C”

Ex.

2x’s antiderivative is x^2 + C.

**The differential (dx):** Just represents that you are taking the integral with RESPECT TO x, t, m, etc.

**The Integrand:** The function you are integrating

**Common Integral Rules:**

**Definite Integral and the Fundamental Theorem of Calculus:**

The area under a graph to the X-axis on a range of [a, b].

Can be Positive OR Negative depending on if it goes under or over the graph.

**Limits of Integration:**

The “a” and “b” values, which is the range of the area.

**Reversal of Limits of Integration:**

“b” should ALWAYS be on top of “a”, and when a is bigger than b, then there is a rule.

**Extra Rules:**

Constant multiplication, sum, and difference rules also work for integrals.

**Weird Rules for Odd and Even functions, with similar limits:**

**Integral of Odd Function:**

As the areas cancel each other out.

**Integral of Even Function:**

The areas are the same so they are just doubled.

**The Seconds Fundamental Theorem of Calculus:**