CHAPTER 44
Multiple Integrals and their Applications
44.1
Evaluate the iterated integral
(x + 2y) dx dy.
Therefore,
44.2
Evaluate the iterated integral
44.3
44.4
44.5
44.6
44.7
44.8
Fig. 44-1
405
44.9
Evaluate
sin y dx dy.
Therefore,
s(sin y)e
cos
(x
2 + y
2 ) dy dx.
Therefore,
Evaluate the iterated integral
sin e dr d6.
Therefore,
(Problem 20.48).
Evaluate the iterated integral
Hence,
Evaluate the iterated integral
dx dy dz.
Hence,
Therefore,
Evaluate
In this case the double integral may be replaced by a product:
(See Problem 44.71.)
6.
Evaluate
Therefore,
Evaluate
dx cannot be evaluated in terms of standard functions. Therefore, we change the order of integration.
using Fig. 44-1.