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Chapter 13: Q 38 (page 1066)

Describe the graphs of the equations and provide alternative equations in the specified coordinate systems.
. Change $ϕ = \frac{3 π}{4}$ to the rectangular and cylindrical systems.

Short Answer

Expert verified

The equation in rectangular coordinates

The equation in cylindrical coordinates

Step by step solution

Step 1:Given information

The given expression is $ϕ = \frac{3 π}{4}$

Simplification

The objective is to convert the equation $ϕ = \frac{3 π}{4}$ into rectangular system

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Most popular questions from this chapter

Find the signed volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane

$f (x, y) = x y W h e r e R = {(x, y) | - 2 \leq x \leq 3, - 1 \leq y \leq 5}$

Let f(x, y, z) and g(x, y, z) be integrable functions on the rectangular solid $R = \{(x, y, z) | a_{1} ⩽ x ⩽ a_{2}, b_{1} ⩽ y ⩽ b_{2}, c_{1} ⩽ z ⩽ c_{2}\}$ . . Use the definition of the triple integral to prove that :

$∭_{R} (f (x, y, z) + g (x, y, z)) d V = ∭_{R} f (x, y, z) d V + ∭_{R} g (x, y, z) d V .$

Earlier in this section, we showed that we could use Fubini’s theorem to evaluate the integral $\int \int_{R} x^{2} y d A$ and we showed that $\int_{2}^{5} \int_{1}^{3} x^{2} y d x d y = 91$ Now evaluate the double integral by evaluating the iterated integral $\int_{1}^{3} \int_{2}^{5} x^{2} y d y d x$ .

Use Definition $13.4$ to evaluate the double integrals in Exercises $29 - 32$ .

$\iint_{R} x y d A$

where

R = {(x, y) ∣ 0 \leq x \leq 2 & 1 \leq y \leq 4}

Discuss the similarities and differences between the definition of the double integral found in Section $13.1$ and the definition of the triple integral found in this section.

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Describe the graphs of the equations and provide alternative equations in the specified coordinate systems.
. Change $ϕ = \frac{3 π}{4}$ to the rectangular and cylindrical systems.

Short Answer

Step by step solution

Step 1:Given information

Simplification

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Describe the graphs of the equations and provide alternative equations in the specified coordinate systems. . Changeϕ=3π4 to the rectangular and cylindrical systems.

Short Answer

Step by step solution

Step 1:Given information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Describe the graphs of the equations and provide alternative equations in the specified coordinate systems.
. Change $ϕ = \frac{3 π}{4}$ to the rectangular and cylindrical systems.