please,
sorry, the region of type I or type II ...something missing?
2 Line Integrals 72 Exercise 2.8.16. Let K be a region of type I or type II and I traj be a path ...
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and y-x2 oriented in the positive direction
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and...
both questions
Use a computer algebra system and the fact that the centroid of the region having area A bounded by the simple closed path C is xd to find the centroid of the region. R: region bounded by the graphs of y -x and y 3 sin θ and outside the circle x-2 cos θ, y-2 sin θ, Evaluate the line integral Let R be the region inside the ellipse x-4 cos θ, y (3x2y + 7) dx +...
Please explain as you solve, thank you! (#1,2 & 4)
an arbillal equation is continuous il nu xo would, for small enough pos This establishes Equation 3. EXERCISES In Exercises 1 to 4, use Green's theorem to compute the value of the line integral y dx + xédy, where y is the indicated closed path. 1. The circle given by g(t) = (cost, sin t), 0 < t < 211 2. The square with corners at (+1, 1), traced counterclock-...
please answer all 3 questions, I need help. thank you
Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $(9x+ ex) dy- (4y + sinh x) dx, where C is the boundary of the square with vertices (2, 0), (5, 0), (5, 3), and (2, 3). $(9x+ ey?) ay- (4y+ + sinhx) dx = 0 (Type an exact answer.) Use Green's Theorem to evaluate the following line integral. i dy - g dx, where (19)...
(a) Let S be the area of a bounded and closed region D with boundary дD of a smooth and simple closed curve, show that S Jlxy -ydx by Green's Theorem. (Hint: Let P--yandQ x) (b) Let D = {(x,y) 1} be an ellipse, compute the area of D a2 b2 (c) Let L be the upper half from point A(a, 0) to point B(-a, 0) along the elliptical boundary, compute line integral I(e* siny - my)dx + (e* cos...
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Let C be the curve consisting of line segments from (0, 0) to (3, 3) to (0, 3) and back to (0,0). Use Green's theorem to find the value of [ xy dx + xy dx + y2 + 3 dy. Use Green's theorem to evaluate line integral fc2x e2x sin(2y) dx + 2x cos(2) dy, where is ellipse 16(x - 3)2 + 9(y – 5)2 = 144 oriented counterclockwise. Use Green's...
0/5 points I Previous Answers 2 Use the flow charts for line integrals and surface integrals to help you decide the best way to find the answer to the following problem Let C be the curve of intersection of x y 4 and x2yv), oriented in the clockwise sense as viewed from the origin. Evaluate y,z, x) dr -167
0/5 points I Previous Answers 2 Use the flow charts for line integrals and surface integrals to help you decide the...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve I = Sc (2y + 7eV*)dx + (3x + cos(y2))dy, where the curve C is the boundary of the region enclosed by the parabolas y = 9x2 and x = y2
1. Let R be the region enclosed by the curves y =ra and r = y2 Nole that there is no med to evaluate any integrals in this problem unless you run out of other things to do). a) Find a dy integral for the volume of the solid obtained by rotating R about the r-axis. (Compare with your solution to part f of the last worksheet). b) Find a dx integral for the volume of the solid obtained by...
I lost in this I need help please thank you
10) [12;8] Let F =(x² - y, x) and C is the boundary of the closed region that is the bounded by the y-axis and the left half of the circle x² + y2 = 4. Assume counterclockwise orientation. (a) Find the work done by this force field on a particle that moves along C, without using Green's Theorem (that is, do it as line integrals: be careful with how...