- 12.1: A contour map is shown for a function on the square . Use a Riemann...
- 12.2: Use the Midpoint Rule to estimate the integral in Exercise 1
- 12.3: Calculate the iterated integral.
- 12.4: Calculate the iterated integral.
- 12.5: Calculate the iterated integral.
- 12.6: Calculate the iterated integral.
- 12.7: Calculate the iterated integral.
- 12.8: Calculate the iterated integral.
- 12.9: Write as an iterated integral, where is the region shown and is an ...
- 12.10: Write as an iterated integral, where is the region shown and is an ...
- 12.11: Describe the region whose area is given by the integral
- 12.12: Describe the solid whose volume is given by the integral and evalua...
- 12.13: Calculate the iterated integral by first reversing the order of int...
- 12.14: Calculate the iterated integral by first reversing the order of int...
- 12.15: Calculate the value of the multiple integral.
- 12.16: Calculate the value of the multiple integral.
- 12.17: Calculate the value of the multiple integral.
- 12.18: Calculate the value of the multiple integral.
- 12.19: Calculate the value of the multiple integral.
- 12.20: Calculate the value of the multiple integral.
- 12.21: Calculate the value of the multiple integral.
- 12.22: Calculate the value of the multiple integral.
- 12.23: Calculate the value of the multiple integral.
- 12.24: Calculate the value of the multiple integral.
- 12.25: Calculate the value of the multiple integral.
- 12.26: Calculate the value of the multiple integral.
- 12.27: Calculate the value of the multiple integral.
- 12.28: Calculate the value of the multiple integral.
- 12.29: Find the volume of the given solid.Under the paraboloid and above t...
- 12.30: Find the volume of the given solid.. Under the surface and above th...
- 12.31: Find the volume of the given solid.The solid tetrahedron with vertices
- 12.32: Find the volume of the given solid.Bounded by the cylinder and the ...
- 12.33: Find the volume of the given solid.One of the wedges cut from the c...
- 12.34: Find the volume of the given solid.Above the paraboloid and below t...
- 12.35: Consider a lamina that occupies the region bounded by the parabola ...
- 12.36: A lamina occupies the part of the disk that lies in the first quadr...
- 12.37: (a) Find the centroid of a right circular cone with height and base...
- 12.38: Find the center of mass of the solid tetrahedron with vertices , , ...
- 12.39: The cylindrical coordinates of a point are . Find the rectangular a...
- 12.40: The rectangular coordinates of a point are . Find the cylindrical a...
- 12.41: The spherical coordinates of a point are . Find the rectangular and...
- 12.42: . Identify the surfaces whose equations are given.
- 12.43: Write the equation in cylindrical coordinates and in spherical coor...
- 12.44: Sketch the solid consisting of all points with spherical coordinate...
- 12.45: Use polar coordinates to evaluate
- 12.46: Use spherical coordinates to evaluate
- 12.47: Rewrite the integral as an iterated integral in the orde
- 12.48: Give five other iterated integrals that are equal to
- 12.49: Use the transformation , to evaluate , where is the square with ver...
- 12.50: Use the transformation , , to find the volume of the region bounded...
- 12.51: Use the change of variables formula and an appropriate transformati...
- 12.52: (a) Evaluate , where is an integer and is the region bounded by the...
Solutions for Chapter 12: Multiple Integrals
Full solutions for Essential Calculus | 2nd Edition
ISBN: 9781133112297
Solutions for Chapter 12
11
4
Summary of Chapter 12: Multiple Integrals
In this chapter we extend the idea of a definite integral to double and triple integrals of functions of two or three variables.
Chapter 12: Multiple Integrals includes 52 full step-by-step solutions. Essential Calculus was written by and is associated to the ISBN: 9781133112297. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Essential Calculus, edition: 2. Since 52 problems in chapter 12: Multiple Integrals have been answered, more than 26509 students have viewed full step-by-step solutions from this chapter.
Key Calculus Terms and definitions covered in this textbook
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Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable
-
Conditional probability
The probability of an event A given that an event B has already occurred
-
Cotangent
The function y = cot x
-
Double-blind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment
-
End behavior asymptote of a rational function
A polynomial that the function approaches as.
-
Equivalent arrows
Arrows that have the same magnitude and direction.
-
Exponential function
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1
-
Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.
-
Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.
-
Index of summation
See Summation notation.
-
Inverse cosine function
The function y = cos-1 x
-
Law of sines
sin A a = sin B b = sin C c
-
Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers
-
Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range
-
Monomial function
A polynomial with exactly one term.
-
Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002
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Parametric curve
The graph of parametric equations.
-
Quartic function
A degree 4 polynomial function.
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Scalar
A real number.
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Sum identity
An identity involving a trigonometric function of u + v