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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. If needed, you can use GeoGebra to graph the region. Also if the evaluation
of the double integral is very complicated, you can use the help of your computer - for example you can use wolfram alpha or symbolab.
F = sin 3y i + cos 7x j; C is the rectangle with vertices at (0, 0),
and 0,
TT

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. If needed, you can use GeoGebra to graph the region. Also if the evaluation
of the double integral is very complicated, you can use the help of your computer - for example you can use wolfram alpha or symbolab.
F = (x2 + y 2) i+ (x - y) j; C is the rectangle with vertices at (0, 0), (6, 0), (6, 9), and (0, 9)
%3D
540
432
-432

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Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. If needed, you can use GeoGebra to graph the region. Also if the evaluation of the double integral is very complicated, you can use the help of your computer - for example you can use wolfram alpha or symbolab. F = (x 2 + y 2) i + (x - y) j; C is the rectangle with vertices at (0, 0), (6, 0), (6, 9), and (0, 9)
Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. If needed, you can use GeoGebra to graph the region. Also if the evaluation of the double integral is very complicated, you can use the help of your computer - for example you can use wolfram alpha or symbolab. F = (x 2 + y 2) i + (x - y) j; C is the rectangle with vertices at (0, 0), (6, 0), (6, 9), and (0, 9) a) 540 b) 432 c) -432 d) 0
The area pab of the ellipse x2/a2 + y2/b2 = 1 can be found by integrating the function ƒ(x, y) = 1 over the region bounded by the ellipse in the xy-plane. Evaluating the integral directly requires a trigonometric substitu-tion. An easier way to evaluate the integral is to use the transforma-tion x = au, y = by and evaluate the transformed integral over the disk G: u2 + y2<= 1 in the uy-plane. Find the area this way.
a. Find the Jacobian of the transformation xu, yuv and sketch the region , in the uv-plane.b. Then use to transform the integral into an integral over G, and evaluate both integrals.
StokesTheorem.Evaluate∫ F·dr,whereF=arctanx/yi+ln√x2+y2j+k and C is the boundary of the triangle with vertices (0, 0, 0), (1, 1, 1), and (0, 0, 2).
Use Green's Theorem to evaluate the line integral. Assume curve is oriented counterclockwise. C is the boundary of the square with vertices (3,1), (6,1), (6,4), and (3,4) Please refer to attached image.
Suppose C is the boundary of region R = {(x, y): x2 ≤ y ≤ x ≤ 1}, oriented counterclockwise (see figure); let F = ⟨1, x⟩. a. Compute the two-dimensional curl of F and determine whetherF is irrotational.b. Find parameterizations r1(t) and r2(t) for C1 and C2, respectively.c. Evaluate both the line integral and the double integral in the circulationform of Green’s Theorem and check for consistency.d. Compute the two-dimensional divergence of F and use the fluxform of Green’s Theorem to explain why the outward flux is 0.
Gauss’s law says that the electric flux through any closed surface is equal to the total chargecontained in the closed surface divided by the permittivity of free space, E0Find the charge contained inside a cube with vertices at (±1, ±1, ±1) when E =< x, y,z >
In Exercises 1–3, sketch the region bounded by the given lines and curves. Then express the region’s area as an iterated double integral and evaluate the integral. 1. The parabola x = -y2 and the line y = x + 2 2. The parabola x = y - y2 and the line y = -x 3. The curve y = ex and the lines y = 0, x = 0, and x = ln 2

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