Integrales Triples

15.4 Triple Integrals in Rectangular Coordinates
24 - q 2

1107

7

2

20.

0 0 0 LLL

q dp dq dr r + 1

spqr-spaced

24. The region inthe first octant bounded by the coordinate planes and the planes x + z = 1, y + 2z = 2
z

Volumes Using Triple Integrals
21. Here is the region ofintegration of the integral
1 1 1-y -1 x 0 L L2 L

dz dy dx .
y

z Top: y Side: 1 y x2 –1 (–1, 1, 0) 1 x (1, 1, 0) 1 z 1

x

25. The region in thefirst octant bounded by the coordinate planes, the plane y + z = 2 , and the cylinder x = 4 - y 2
z

y

Rewrite the integral as an equivalentiterated integral in the order a. dy dz dx c. dx dy dz e. dz dx dy. 22. Here is the region of integration of the integral
1 0 y2

b. dy dx dz d. dx dz dy

yx

0 -1 0 LL L

dz dy dx.
z 1 y2

(0, –1, 1) (1, –1, 1) z

26. The wedge cut from the cylinder x 2 + y 2 = 1 by the planes z = -y and z = 0z

0 (1, –1, 0) x 1

y y x

Rewrite the integral as an equivalent iterated integral in the order a. dy dz dx c. dx dy dz e. dz dx dy. Find thevolumes of the regions in Exercises 23–36. 23. The region between the cylinder z = y 2 and the xy-plane that is bounded by the planes x = 0, x = 1, y = -1, y =1
z

b. dy dx dz d. dx dz dy 27. The tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1, 0, 0), (0, 2,0), and (0, 0, 3).
z (0, 0, 3)

y x

(1, 0, 0) x

(0, 2, 0) y

Copyright © 2005 Pearson Education, Inc., publishing as Pearson Addison-Wesley