- 13.1: In 1 through 5, evaluate the given integral by first revirsing the ...
- 13.2: In 1 through 5, evaluate the given integral by first revirsing the ...
- 13.3: In 1 through 5, evaluate the given integral by first revirsing the ...
- 13.4: In 1 through 5, evaluate the given integral by first revirsing the ...
- 13.5: In 1 through 5, evaluate the given integral by first revirsing the ...
- 13.6: The double integral I I - r/r',/.r' J,, J. \ is an improper integra...
- 13.7: Find the volume of the soiid f that lies below the paraboloid : : ,...
- 13.8: Find by integration in cylindrical coordinates the volume bounded b...
- 13.9: Use integration in spherical coordinates to find the volume and cen...
- 13.10: Find the volunre of the solid bounded by the elliptic paraboloids :...
- 13.11: Find the volume bounded by the paraboloid l = .tr + 3:r and the par...
- 13.12: Find the volume of the region bounded by the parabolic cylinders: =...
- 13.13: Find the volume of the region bounded by the elliptical cylinder r ...
- 13.14: Show that the volume of the solid bounded by the elliptical cylinde...
- 13.15: Lel R be the first-quadrant region bounded by the curve .rr + rlt :...
- 13.16: The region bounded by l = .rr and r = r'r: 6(r.r') : ..: + .r'l
- 13.17: The region bounded by,r : 2,r'r and r': : -r - 4: 6(.r. r') = j-
- 13.18: The region between r' = ln-r and the,t-axis over the interval llr !...
- 13.19: The circle bounded bv r' : 2 cos d: 6 (r'. 0) = ,t (3 senstanll
- 13.20: The legion of 19: d(r. 0) : r
- 13.21: , Use the iirst theorem of Pappus to lind the r,-coordinate of rhe ...
- 13.22: (a) Use the nrst theorem of Pappus to find the centroid of the firs...
- 13.23: Find the centroid of the region in the 5-plane bounded by the .r-ax...
- 13.24: Find the volume of the solid that lies below the paraboiic cylinder...
- 13.25: Use cylindrical coordinates to Rnd the volume of the icecream cone ...
- 13.26: . Find the volume and centrcid of the ice-cream cone bounded above ...
- 13.27: A homogeneous solid circular cone has mass M and base radius a. Fin...
- 13.28: Find the mass of the iirst octant of the ball p ! a if its densily ...
- 13.29: Find the moment of inenia around the r-axis of the homogeneous soli...
- 13.30: Find the volume of the region in the first octant rhar is bounded b...
- 13.31: Find the moment of inenia around the --axis of the homogeneous regi...
- 13.32: Find the volume of the solid obtained by revolving around the )-axi...
- 13.33: Find the volume of the solid obtained by revolving around the .jr-a...
- 13.34: Find the volume of the solid torus obtained by revolving the disk 0...
- 13.35: Assume that the to.us of has uniform density 6. Find its moment of ...
- 13.36: Show thal the average distance o[ the pninrs ota disk of radiu\ d f...
- 13.37: Show that the average distance of the points of a disk of radius (l...
- 13.38: A circle of radius I is interior to and tangent to a circle of radi...
- 13.39: Show that the average distance of the points of a spherical ball of...
- 13.40: Show that the average distance of the points of a spherical ball of...
- 13.41: A sphere of radius I is interior to and tangent to a sphere of radi...
- 13.42: A right circular cone has radius R and height 11. Find the average ...
- 13.43: A right circular cone has radius R and height 11. Find the average ...
- 13.44: Find the surface area of the pan of the sudace a = J'r - r: that is...
- 13.45: Let A be the suface area of the zone on the sphere p : d between th...
- 13.46: Find the surface area of the pan of the sphere p = 2 that is inside...
- 13.47: A square hole \\'ith side length 2 is cut through a cone of height ...
- 13.48: Numerical)y approximate the surface area ol the part of the parabol...
- 13.49: A "fence" of Variable height h0) stands above the plane curve (r (t...
- 13.50: Apply the formula of .19 to compute rhe area of the pan ofthe cylin...
- 13.51: Find the polar moment of inertia ol the lirst-quadrant region ol co...
- 13.52: Substitute rr :.\- - 1, and r) :.r + ] to evaluate ll /r'-1\ / / ex...
- 13.53: Use el)ipsoidal coordinates .r - .tpsindcos0. -1. = bp sin @ sin e....
- 13.54: . Let R be the firsGquadrant rcgion bounded by the lemniscates 12 :...
- 13.55: A 2-by-2 square hole is cur symmelrically rhrough a sphere of radiu...
- 13.56: Show that the volume enclosed by the surface r1l3 + ),2/3 +,1/3 _ a...
- 13.57: Show that the volume enclosed by the surface lrlr 3 + lll' J + lrlr...
- 13.58: Find the average of the squarc of the distance of points of rhe sol...
- 13.59: A cube C of edge length 1 is rotated around a line passing through ...
Solutions for Chapter 13: Multiple lntegrals
Full solutions for Calculus:Early Transcendentals | 7th Edition
ISBN: 9780131569898
Summary of Chapter 13: Multiple lntegrals
A multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z).
Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Chapter 13: Multiple lntegrals includes 59 full step-by-step solutions. Since 59 problems in chapter 13: Multiple lntegrals have been answered, more than 40425 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7.
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Bearing
Measure of the clockwise angle that the line of travel makes with due north
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Common logarithm
A logarithm with base 10.
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Compounded monthly
See Compounded k times per year.
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Double-blind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment
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equation of an ellipse
(x - h2) a2 + (y - k)2 b2 = 1 or (y - k)2 a2 + (x - h)2 b2 = 1
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Grapher or graphing utility
Graphing calculator or a computer with graphing software.
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Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.
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Horizontal line
y = b.
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Inverse tangent function
The function y = tan-1 x
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Linear system
A system of linear equations
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Logarithmic regression
See Natural logarithmic regression
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Natural logarithm
A logarithm with base e.
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Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.
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Pseudo-random numbers
Computer-generated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random
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Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.
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Subtraction
a - b = a + (-b)
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Time plot
A line graph in which time is measured on the horizontal axis.
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Variation
See Power function.
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Vertical stretch or shrink
See Stretch, Shrink.
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xy-plane
The points x, y, 0 in Cartesian space.