Use Green's Theorem to evaluate | (y? – tan-1 x²)dx + (3xy + 4x – In (y² + 4))dy where C is the triangular path starting from (0,0), going to (6,4), then (4,0) and back to (0,0).

Q: Use Green Theorem to evaluate C P xydx+e'dy where Cis the path from (0,0) to (1,1) along the graph…

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Q: Evaluate I = Se(sin a + 8y) dx + (9x + y) dy for the nonclosed path ABCD in the figure. C А — (0,…

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Q: x y 11. Use Green's theorem to evaluate O In(1+ y) dx –- dy , where C is the triangle with vertices…

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Q: Evaluate | (transparent gamma symbol) ∫(x2 + y2) dz | where z = x + iy with (transparent gamma…

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Q: Sketch the strophoid shown below. r= sec(0)- 2 cos(8), -<0 < x/2 1.0 1.0 0.5 0.5 -10 -0.5 0.5 1.0…

A: A strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the…

Q: The integral ∫C[(3x2y+y2)dx+(x3+2xy)dy] is independent of the path. Evaluate the integral where C is…

A: Given: R=ti+(t2+t-2)j   for 0&lt;=t&lt;=2

Q: Find the line integral ye-xz ds Here, C is the path r(t) = [t,3t,-6t], 0sts In(8) ·

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Q: Use Green's Theorem to evaluate the line integral |v - x)dx + (2x – y)dy for the given path. C: x =…

A: Answer

Q: Use Green's Theorem to evaluate (y? tan- a?) dx + (3.xy+ 4x – In(y² + 4)) dy, where C is the…

A: We need to evaluate integral.

Q: Verify Green's Theorem by evaluating both integrals y2 dx + x² dy = dA ду for the given path. C:…

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

Q: Evaluate eVf •dr where f(r,y, 2) = 4rye² and C is the path parameterized by r(t) = cos² t i +…

A: Given: fx,y,z=4xyezrt=cos2ti+sin2tj+tantk0≤t≤π4 Formulas used: ddxxn=nxn-1ddxex=exddxfgx=f'gx·g'x…

Q: Evaluate f(x + 2y)dx + (y – 2x)dy around the ellipse C defined by x = 4 cos 0, y = 3 sin 0,0 < 0 <…

A: Given the Integral : ∮c(x+2y)dx-(y-2x)dy ⇒Let I=∫C(x+2y,y-2x).(dx,dy) , x=4cosθ and y=3sinθ…

Q: Use Green's Theorem to evaluate the integral (y - x)dx + (2x - y)dy for the given path. C: x = 2…

A: Definition used -                                According to the green theorem -…

Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x – y)dy for the given path. C: x =…

A: Let's find.

Q: 3. Calculate the line integral S F - d7, where F = (x²y³, x³y?) and C is the path given by C 7(t) =…

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Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

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Q: Evaluate Vf dr where f(x, y, z) = 4xye and C is the path parameterized by r(t) = costi+ sin tj+tant…

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Q: Evaluate I = fc (sin(x) + 4y) dx + (9x + 7y) dy for the nonclosed path ABCD in the figure.

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy = / / dA ax for the given path. C:…

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Q: Show that the integral S. (3x²y + y)dx + (x3 + x)dy is independent of path, if it is, then evaluate…

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Q: Evaluate the line integral f. F. dr where F = (2 sin a,–5 cos y, 10xz) and C is the path given by…

A: We will evaluate the given line integral.

Q: 2. Find the value of xy dx + Vy2 + 1dy, where C is the path shown on the graph below. (Hint: Use…

A: We have to find the value of  ∫Cxy dx + y2+1 dy. Given the path C is

Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: Compute I = (2x²132²y+ 4xy)ax +(x'+2x²-y') dy+zdz along The curve C C4U Cz UG given in the figure…

A: Given To compute I=∫C2x3+3x2y+4xy.dx+x3+2x2-y2dy+zdz along the curve C=C1∪C2∪C3 given in the figure.

Q: Use Green Theorem to evaluate P xydx+edy where Cis C the path from (0,0) to (1,1) along the graph of…

A: The correct option is (d). Partially differentiate M and N w.r.t y and x respectively.

Q: Use Green Theorem to evaluate $ xydx+e'dy where C is the path from (0,0) to (1,1) along the graph of…

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Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x – y)dy for the given path. C: x =…

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Q: 39. Show that the graph of r =t sin ti + t cos tj + t'k lies on the paraboloid z = x² + y².

A: Here we compare r as its basic equation to prove this.

Q: f (lnx + y) dx − a² dy, where & is the rectangle with vertices (1, 1), 1. Use Green's Theorem to…

A: Let I =∮(ln x+y)dx-x2 dy, where the region is C which is a rectangle with vertices…

Q: Use Greens Theorem to evaluate: §. (2x + ev´)dy - (4y2 + e*")dx where C is the boundary of the…

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Q: 15. Evaluate the line integral J. (3x²y* - 6xy ]dx + (4x²y³ - 3x°) dv, where C is any path from…

A: My=Nx means F is conservative vector field

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Use Green's Theorem to evaluate | (v? – tan-1 x²)dx + (3xy + 4x – In (y2 + 4))dy where C is the…

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: Find the solution of the following Cauchy problem and sketch its graph at t = 0,0.5, 1, 1.5, 2 &…

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Q: Use Green's Theorem to evaluate the line integra Icon (y − x)dx + (2x − y)dy - - for the given path.…

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Q: Verify Green's Theorem by evaluating both integrals aN aM y2 dx + x2 dA ду ax for the given path. C:…

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Q: Let P denote the path r(t) = (7cost), where 0<t< 2n, and compute ſpF - dĩ where F = (!+ty 4 sin…

A: Let F→x,y be a vector field and r→t=xt,yt be the path of an object, where t1≤t≤t2. The line integral…

Q: Use Green's Theorem to evaluate x dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: Evaluate I = f.(sin x + 9y) dx + (7x + y) dy for the nonclosed path ABCD in the figure. D= (0,9) C А…

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Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x - y)dy for the given path. C: x =…

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Q: Consider the 2nd order PDE -3u +6xu-3u w=cos(x). XX ху yy (a Determine the regions in the xy-plane…

A: Consider the PDE: -3uxx+6xuxy-3uyy=cosx. A second order PDE of the form…

Q: Show that the graph of ř = (t sin t, t cos t, t²) lies on the paraboloid z = x? + y?.

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Q: Use Green's Theorem to evaluate x' dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: 1. Use a change of variables to evaluate [[ y- dA where R is the trapezoid with vertices (1,0,…

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Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

Q: Use Green's theorem to evaluate f (x²y) dx + y²dy here C is close path formed y = x and y = x³ from…

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Q: 1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,…

A: Given: The function with two polygonal paths in space joining the origin to the point (1, 1, 1).…