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”
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.
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: