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Chapter 13: Q 12. (page 1066)

To convert from spherical to cylindrical coordinates:
$r = - - - -, θ = - - - -, z = - - - -$

Short Answer

Expert verified

$r = ρ \sin ϕ, θ = θ, z = ρ \cos ϕ$

Step by step solution

Given Information

Given $(r, θ, z)$ be cylindrical coordinates and $(ρ, θ, ϕ)$ be spherical coordinates.

Simplification

The relation between two is:

$r = ρ \sin ϕ, θ = θ, z = ρ \cos ϕ$

Hence,

$r = ρ \sin ϕ$

$θ = θ$

and

$z = ρ \cos ϕ$

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Most popular questions from this chapter

Describe the three-dimensional region expressed in each iterated integral:

$\int_{- 2}^{4} \int_{2}^{6} \int_{0}^{5} f (x, y, z) d y d x d z$

Evaluate each of the double integrals in Exercises $37 - 54$ as iterated integrals.

localid="1650380493598" $\int \int_{R} \sin (2 x + y) d A,$

wherelocalid="1650380496793" $R = \{(x, y) | 0 \leq x \leq \frac{π}{2} a n d 0 \leq y \leq \frac{π}{2}\}$

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32

$\int \int_{R} x^{2} y d A W h e r e R = {(x, y) | - 1 \leq x \leq 0, 0 \leq y \leq 2}$

Explain why it would be difficult to evaluate the double integrals in Exercises 18 and 19 as iterated integrals.

$\int \int_{R} \cos (x y) d A w h e r e R = \{(x, y) I \frac{π}{4} \leq x \leq \frac{π}{2} a n d \frac{π}{2} \leq y \leq π\}$

Evaluate each of the double integrals in Exercises $37 - 54$ as iterated integrals.

role="math" localid="1650327788023" $\int \int_{R} y \sin x d A,$

whererole="math" localid="1650327080219" $R = \{(x, y) | 0 \leq x \leq \frac{π}{2} a n d 0 \leq y \leq 1\}$

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To convert from spherical to cylindrical coordinates:
$r = - - - -, θ = - - - -, z = - - - -$

Short Answer

Step by step solution

Given Information

Simplification

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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To convert from spherical to cylindrical coordinates:r=----,θ=----,z=----

Short Answer

Step by step solution

Given Information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

To convert from spherical to cylindrical coordinates:
$r = - - - -, θ = - - - -, z = - - - -$