 15.4.1: Which of the following represent the integral of f (x, y) = x2 + y2...
 15.4.2: What are the limits of integration in f (r, , z)r dr d dz if the in...
 15.4.3: What are the limits of integration in f ( , , ) 2 sin d d d if the ...
 15.4.4: An ordinary rectangle of sides x and y has area x y, no matter wher...
 15.4.5: In Exercises 16, sketch the region D indicated and integrate f (x, ...
 15.4.6: In Exercises 16, sketch the region D indicated and integrate f (x, ...
 15.4.7: In Exercises 714, sketch the region of integration and evaluate by ...
 15.4.8: In Exercises 714, sketch the region of integration and evaluate by ...
 15.4.9: In Exercises 714, sketch the region of integration and evaluate by ...
 15.4.10: In Exercises 714, sketch the region of integration and evaluate by ...
 15.4.11: In Exercises 714, sketch the region of integration and evaluate by ...
 15.4.12: In Exercises 714, sketch the region of integration and evaluate by ...
 15.4.13: In Exercises 714, sketch the region of integration and evaluate by ...
 15.4.14: In Exercises 714, sketch the region of integration and evaluate by ...
 15.4.15: In Exercises 1520, calculate the integral over the given region by ...
 15.4.16: In Exercises 1520, calculate the integral over the given region by ...
 15.4.17: In Exercises 1520, calculate the integral over the given region by ...
 15.4.18: In Exercises 1520, calculate the integral over the given region by ...
 15.4.19: In Exercises 1520, calculate the integral over the given region by ...
 15.4.20: In Exercises 1520, calculate the integral over the given region by ...
 15.4.21: Find the volume of the wedgeshaped region (Figure 18) contained in...
 15.4.22: Let W be the region above the sphere x2 + y2 + z2 = 6 and below the...
 15.4.23: Evaluate D x2 + y2 dA, where D is the domain in Figure 20. Hint: Fi...
 15.4.24: Evaluate D x x2 + y2 dA, where D is the shaded region enclosed by th
 15.4.25: Let W be the region above the plane z = 2 and below the paraboloid ...
 15.4.26: Use cylindrical coordinates to calculate the integral of the functi...
 15.4.27: In Exercises 2732, use cylindrical coordinates to calculate W f (x,...
 15.4.28: In Exercises 2732, use cylindrical coordinates to calculate W f (x,...
 15.4.29: In Exercises 2732, use cylindrical coordinates to calculate W f (x,...
 15.4.30: In Exercises 2732, use cylindrical coordinates to calculate W f (x,...
 15.4.31: In Exercises 2732, use cylindrical coordinates to calculate W f (x,...
 15.4.32: In Exercises 2732, use cylindrical coordinates to calculate W f (x,...
 15.4.33: In Exercises 3336, express the triple integral in cylindrical coord...
 15.4.34: In Exercises 3336, express the triple integral in cylindrical coord...
 15.4.35: In Exercises 3336, express the triple integral in cylindrical coord...
 15.4.36: In Exercises 3336, express the triple integral in cylindrical coord...
 15.4.37: Find the equation of the rightcircular cone in Figure 22 in cylind...
 15.4.38: Use cylindrical coordinates to integrate f (x, y, z) = z over the i...
 15.4.39: Find the volume of the region appearing between the two surfaces in...
 15.4.40: Use cylindrical coordinates to find the volume of a sphere of radiu...
 15.4.41: Use cylindrical coordinates to show that the volume of a sphere of ...
 15.4.42: Use cylindrical coordinates to find the volume of the region bounde...
 15.4.43: Use spherical coordinates to find the volume of the region bounded ...
 15.4.44: Use spherical coordinates to find the volume of a sphere of radius ...
 15.4.45: In Exercises 4550, use spherical coordinates to calculate the tripl...
 15.4.46: In Exercises 4550, use spherical coordinates to calculate the tripl...
 15.4.47: In Exercises 4550, use spherical coordinates to calculate the tripl...
 15.4.48: In Exercises 4550, use spherical coordinates to calculate the tripl...
 15.4.49: In Exercises 4550, use spherical coordinates to calculate the tripl...
 15.4.50: In Exercises 4550, use spherical coordinates to calculate the tripl...
 15.4.51: Use spherical coordinates to evaluate the triple integral of f (x, ...
 15.4.52: Find the volume of the region lying above the cone = 0 and below th...
 15.4.53: Calculate the integral of f (x, y, z) = z(x2 + y2 + z2) 3/2 over th...
 15.4.54: Calculate the volume of the cone in Figure 22, using spherical coor...
 15.4.55: Calculate the volume of the sphere x2 + y2 + z2 = a2, using both sp...
 15.4.56: Let W be the region within the cylinder x2 + y2 = 2 between z = 0 a...
 15.4.57: BellShaped Curve One of the key results in calculus is the computa...
 15.4.58: An Improper Multiple Integral Show that a triple integral of (x2 + ...
 15.4.59: Prove the formula D ln r dA = 2 where r = x2 + y2 and D is the unit...
 15.4.60: Recall that the improper integral 1 0 xa dx converges if and only i...
Solutions for Chapter 15.4: Integration in Polar, Cylindrical, and Spherical Coordinates
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 15.4: Integration in Polar, Cylindrical, and Spherical Coordinates
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Chapter 15.4: Integration in Polar, Cylindrical, and Spherical Coordinates includes 60 full stepbystep solutions. Since 60 problems in chapter 15.4: Integration in Polar, Cylindrical, and Spherical Coordinates have been answered, more than 40906 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This expansive textbook survival guide covers the following chapters and their solutions.

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

Coordinate plane
See Cartesian coordinate system.

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Graphical model
A visible representation of a numerical or algebraic model.

Inverse variation
See Power function.

Lemniscate
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

Modified boxplot
A boxplot with the outliers removed.

Multiplicative inverse of a matrix
See Inverse of a matrix

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Perihelion
The closest point to the Sun in a planetâ€™s orbit.

Period
See Periodic function.

Perpendicular lines
Two lines that are at right angles to each other

Quadratic regression
A procedure for fitting a quadratic function to a set of data.

Quadric surface
The graph in three dimensions of a seconddegree equation in three variables.

Response variable
A variable that is affected by an explanatory variable.

Secant
The function y = sec x.

Seconddegree equation in two variables
Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.

Solution set of an inequality
The set of all solutions of an inequality

Xscl
The scale of the tick marks on the xaxis in a viewing window.