Fundamental Theorem of Calculus

1. 1. An antiderivative of a function [latex]f[/latex] is one function [latex]F[/latex] whose derivative is [latex]f[/latex].

      OR

      [latex]F(x)[/latex] is the antiderivative of [latex]f(x)[/latex]

      For example:

      

      [table id=8 /]

       

1. A definite integral equals the difference between the antiderivative of the bounds of the definite integral

[latex]F(b)\;-:F(a)\;=:\int_{c}^{b} f(t) dt\;-:\int_{c}^{a} f(t) dt\;=:\int_{b}^{a} f(t) dt[/latex]

Images: https://www.khanacademy.org