Calculus I / AP Calculus AB Purpose: To formally define the definite integral, interpret it geometrically, and understand its basic properties.

: [ \int_a^b [f(x) \pm g(x)] , dx = \int_a^b f(x) , dx \pm \int_a^b g(x) , dx ] [ \int_a^b k f(x) , dx = k \int_a^b f(x) , dx ]

: This introduces the concept of Section 5.2: Sigma Notation and Limits of Finite Sums . By adding up these infinitely small pieces, we can eventually describe the "total" amount eaten using a single number: a definite integral. 2. Building the Area with Riemann Sums