Problem. 12.1 : Write the equation of the surface in rectangular coordinates. x^2/9+y^2/4
Problem. 12.1 : Write the equation of the surface in rectangular coordinates. x^2/9+y^2/4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem. 12:** Consider the surface with parametric equations
\[
x = 3u \cos(v), \quad y = 2u \sin(v), \quad z = u^2, \quad 0 \leq u \leq 2, \quad 0 \leq v \leq 2\pi
\]
Set up a double integral for the area of the surface.
\[
A(S) = \int_{0}^{2\pi} \int_{0}^{2} 2u \sqrt{4u^2 \cdot \alpha} \, du \, dv
\]
**Problem. 12.1:** Write the equation of the surface in rectangular coordinates.
\[
z = \frac{x^2}{9} + \frac{y^2}{4}
\]
**Problem. 12.1.1:** Set up another double integral for the surface area in rectangular coordinates.
\[
A(S) = \int_{?}^{?} \int_{?}^{?} \, \, ? \, dy \, dx
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Transcribed Image Text:**Problem. 12:** Consider the surface with parametric equations
\[
x = 3u \cos(v), \quad y = 2u \sin(v), \quad z = u^2, \quad 0 \leq u \leq 2, \quad 0 \leq v \leq 2\pi
\]
Set up a double integral for the area of the surface.
\[
A(S) = \int_{0}^{2\pi} \int_{0}^{2} 2u \sqrt{4u^2 \cdot \alpha} \, du \, dv
\]
**Problem. 12.1:** Write the equation of the surface in rectangular coordinates.
\[
z = \frac{x^2}{9} + \frac{y^2}{4}
\]
**Problem. 12.1.1:** Set up another double integral for the surface area in rectangular coordinates.
\[
A(S) = \int_{?}^{?} \int_{?}^{?} \, \, ? \, dy \, dx
\]
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