Evaluate the double integral
where D is the triangular region with vertices
(0, 0), (5, 0), (0, 4).

50/3

The work

4.

Find the volume of the solid bounded by the planes
x = 0, y = 0, z = 0, and x + y + z = 2.

4/3

The work

5.

Consider the integral
.
Sketch the region of integration and change the order of integration.

a = b =

a = 0
b = 9
0
y/9

The work

6.

Consider the integral
.
Sketch the region of integration and change the order of integration.

a = b =

a = 0
b = 42
(y^2)/36
49

The work

7.

Consider the integral
.
If we change the order of integration we obtain the sum
of two integrals:

a = b =

c = d =

a = 0
b = 5.477
0
6
c = 5.477
d = 6
0
36-x^2

The work

8.

Consider the integral
.
Sketch the region of integration and change the order of integration.

a = b =

a = 0
b = 6.91

e^(y/3)
10

The work

9.

In evaluating a double integral over a region, a sum of iterated
integrals was obtained as follows:

Sketch the region D and express the double integral as an iterated integral
with reversed order of integration.

a = b =

a = 0
b = 4

x
8-x

The work

10.

Evaluate the integral by reversing the order of integration.

8.36*10^33

The work

11.

Evaluate the integral by reversing the order of integration.

-0.072

The work

12.

Here is a more interesting problem to consider.
We want to evaluate the improper integral
Do it by rewriting the numerator of the integrand as for appropriate f, g, h and then reversing the order of
integration in the resulting double integral.