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# Solutions for Chapter 12: Multiple Integrals ## Full solutions for Essential Calculus | 2nd Edition

ISBN: 9781133112297 Solutions for Chapter 12: Multiple Integrals

Solutions for Chapter 12
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##### ISBN: 9781133112297

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
• 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

• Parametric curve

The graph of parametric equations.

• Quartic function

A degree 4 polynomial function.

• Scalar

A real number.

• Sum identity

An identity involving a trigonometric function of u + v