 15.1: Suppose is a continuous function defined on a rectangle . (a) Write...
 15.2: (a) How do you define if is a bounded region that is not a rectangl...
 15.3: How do you change from rectangular coordinates to polar coordinates...
 15.4: If a lamina occupies a plane region and has density function , writ...
 15.5: Let be a joint density function of a pair of continuous random vari...
 15.6: Write an expression for the area of a surface with equation .
 15.7: (a) Write the definition of the triple integral of over a rectangul...
 15.8: Suppose a solid object occupies the region and has density function...
 15.9: (a) How do you change from rectangular coordinates to cylindrical c...
 15.10: (a) If a transformation is given by , what is the Jacobian of ? (b)...
 15.11: Describe the region whose area is given by the integral
 15.12: Describe the solid whose volume is given by the integral and evalua...
 15.13: Calculate the iterated integral by first reversing the order of int...
 15.14: Calculate the iterated integral by first reversing the order of int...
 15.15: Calculate the value of the multiple integral. , where ,
 15.16: Calculate the value of the multiple integral. , where ,
 15.17: Calculate the value of the multiple integral. , where is bounded by...
 15.18: Calculate the value of the multiple integral. , where is the triang...
 15.19: Calculate the value of the multiple integral. , where is the region...
 15.20: Calculate the value of the multiple integral. , where is the region...
 15.21: Calculate the value of the multiple integral. , where is the region...
 15.22: Calculate the value of the multiple integral. , where is the region...
 15.23: Calculate the value of the multiple integral. , where , ,
 15.24: Calculate the value of the multiple integral. , where is the solid ...
 15.25: Calculate the value of the multiple integral. , where is bounded by...
 15.26: Calculate the value of the multiple integral. , where is bounded by...
 15.27: Calculate the value of the multiple integral. , where lies above th...
 15.28: Calculate the value of the multiple integral. , where is the solid ...
 15.29: Find the volume of the given solid. Under the paraboloid and above ...
 15.30: Find the volume of the given solid. Under the surface and above the...
 15.31: Find the volume of the given solid. The solid tetrahedron with vert...
 15.32: Find the volume of the given solid. Bounded by the cylinder and the...
 15.33: Find the volume of the given solid. One of the wedges cut from the ...
 15.34: Find the volume of the given solid. Above the paraboloid and below ...
 15.35: Consider a lamina that occupies the region bounded by the parabola ...
 15.36: A lamina occupies the part of the disk that lies in the first quadr...
 15.37: (a) Find the centroid of a right circular cone with height and base...
 15.38: Find the area of the part of the cone between the planes and .
 15.39: Find the area of the part of the surface that lies above the triang...
 15.40: Graph the surface , , , and find its surface area correct to four d...
 15.41: Use polar coordinates to evaluate
 15.42: Use spherical coordinates to evaluate ;
 15.43: If is the region bounded by the curves and , find the approximate v...
 15.44: Find the center of mass of the solid tetrahedron with vertices , , ...
 15.45: The joint density function for random variables and is (a) Find the...
 15.46: A lamp has three bulbs, each of a type with average lifetime 800 ho...
 15.47: Rewrite the integral as an iterated integral in the order .
 15.48: Give five other iterated integrals that are equal to
 15.49: Use the transformation , to evaluate where is the square with verti...
 15.50: Use the transformation , , to find the volume of the region bounded...
 15.51: Use the change of variables formula and an appropriate transformati...
 15.52: The Mean Value Theorem for double integrals says that if is a conti...
 15.53: Suppose that is continuous on a disk that contains the point . Let ...
 15.54: (a) Evaluate , where is an integer and is the region bounded by the...
Solutions for Chapter 15: MULTIPLE INTEGRALS
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 15: MULTIPLE INTEGRALS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 15: MULTIPLE INTEGRALS includes 54 full stepbystep solutions. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. Since 54 problems in chapter 15: MULTIPLE INTEGRALS have been answered, more than 22638 students have viewed full stepbystep solutions from this chapter.

Annuity
A sequence of equal periodic payments.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Completing the square
A method of adding a constant to an expression in order to form a perfect square

Domain of a function
The set of all input values for a function

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

Fibonacci numbers
The terms of the Fibonacci sequence.

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Identity properties
a + 0 = a, a ? 1 = a

Index of summation
See Summation notation.

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

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Rational expression
An expression that can be written as a ratio of two polynomials.

Reflection across the yaxis
x, y and (x,y) are reflections of each other across the yaxis.

Row operations
See Elementary row operations.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Speed
The magnitude of the velocity vector, given by distance/time.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.