Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

Q: Suppose w = In(x² + y² + z²) , x = ue³" sin(9v) , y = ue3" cos(9v), and z = ued". %3D Compute dw/du…

A: If w is a function of three variables, such that w(x,y,z) and x, y and z are further function of u…

Q: Evaluate the line integral / (x+ 2- rom (0,0) to (3, 0), the path C2 fro co (0,0) by applying the…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

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Q: Evaluate the integra ∮C -y3 dy + x3 dx for any closed path C.

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

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

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Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

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 =…

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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: 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: 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: Find the solution for the damped motion. my'' + cy' + ky = 0 with m = 10, k = 90, y(0) = 0.16,…

A: The differential equation of the damped motion is  my''+cy'+ky=0 with m=10, k=90 and c=10 That…

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

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Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Introduction: The parametrization is a very significant part that is related to vector calculus.…

Q: Evaluate the line integral fe y dx + x dy where C is the parameterized path x = , y = f, 3 <iS9.…

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Q: 14. Calculate | (y? – z)dx + (2ry)dy+(2z-x)dz where C is the path along (t2 + 4t + 2, V4+ 5t, t –…

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Q: am dA y² dx + x² dy = / / ( - əx ду for the given path. hC: rectangle with vertices (0, 0), (2, 0),…

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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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: Express the curve by an equation in x and y given x(t) = sin(t) and y(t) = 8 + cos² (t). a) O-x² +y…

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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: 17. Integrate f(x, y, z) = (x + y + z)/(x² + y² + z²) over the path r(t) = ti + tj + tk, 0 < a < t<…

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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: If C is the line segment from (1,3) to, (0, 0), find the value of the line integral: S(3y² i +3x}) ·…

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Q: Use the Chain Rule to find dz/əs and dz/at. z = tan(u/v), u = 8s + 3t, V = 3s 8t az as az Ət II

A: Given data: *z=tan(uv) *u=8s+3t and v=3s-8t The partial derivative of z with respect to s is given…

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

A: Let's find.

Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: Exercise 1.3.2 Give a paramatrization for the curve curve y = x³ + ()x-¹, then deduce the length of…

A: Given curve is  y=16x3+12x-1

Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Given Path C is C1:  y=x+3,     0≤x≤4C2:  y=x2,         y=7 to y=0C3:  line connecting C1 and C2…

Q: Evaluate I = Jc(sin ¤ + 2y) dx + (2x + y) dy for the nonclosed path ABCD in the figure. D А 3 (0,0),…

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Q: -2-x Q1) Evaluate the integral S* dy dx using polar coordinate 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: 1 Check xyz? dx +a²z² dy + x²yz dz for path independence. 1 Does xyz? dx +x²z² dy + x²yz dz Yesv…

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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: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

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Q: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

Q: Eveluake F.dv wlere flaiy,z) where the segnent on Cis (-',2,0) to (3,0,1)

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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: 3. Show that the line integral | (r + y)dx + xdy is independent of path and evaluate this integral…

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: 7. Let F = (2x sin(y)e", x² cos(y)e*, z² sin(y)e*). Find along the path c:T = (sin(t), t, cos(t))…

A: F=2xsinyez, x2cosyez, x2sinyez curlF=ijk∂∂x∂∂y∂∂z2xysinyezx2cosyezx2sinyez⇒curlF=0 So, F is a…

Q: 8. Evaluate the line integral fx'dx + xe 'dy where C is the closed path along the triangle in the…

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Q: Evaluate the line integral y dx + x dy where C is the parameterized path x = = ² , y = t° , 3 -ydx +…

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