Section 5.3
Fundamental Theorem of Calculus
Topic 1:
Area Functions
Definition
Area Function
Let
𝑓
be a continuous function for
𝑡 ≥ ?
.
The
area function
for
𝑓
with left endpoint
?
is
𝐴(𝑥) = ∫ 𝑓(𝑡) 𝑑𝑡
𝑥
?
,
where
𝑥 ≥ ?
.
The area function gives the net area of the region bounded by the graph of
𝑓
and the
𝑡
-axis on the interval
[?, 𝑥]
.