 
Summary: 15.1 Double integrals over Rectangles
Motivation:
Volume under a surface ( , ) 0z f x y=
In Math 102, we did
area problem  definite integration of f(x)
Here we see that
volume problem  double integration over a region R
The double integral of f over the rectangle R is
,
1 1
( , ) lim ( , )
m n
i j
m n
i jR
f x y dA f x y A
= =
=
1
