1 /(-))). i 2x²y² xy³ Evaluate the integral curve joining (1, 2) to (2, 2). Enter an exact answer. j. dr using the potential function f(x, y) = = 1 2xy²' where C is any

Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).

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Q: 23. Evaluate Jcxy dx + (x + y) dy along the curve y = x² from (-1, 1) to (2, 4).

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Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

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Q: 13. Verify that F(x, y) = (exy + y)i + (ex+x) j is conservative. Find a potential function for F.

A: Given: Fx, y=exy+yi+ex+xj (a) To verify F is conservative. (b) To find potential function for F.

Q: Exercises (13): Evaluate the following integrals 1. x²e*dx

A: As per bertleby guide line I have to solve the first question only,  please resubmit the other…

Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

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Q: DATE Find the differential of the given function. ose the best answer a) dy: -x) dx xp (x-1)

A: here option B is true

Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: consists of y = 4-x and straight line from (-2,0) to (2,0). Sketch the curve C. 64 ans: 3

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Q: The area of the surface obtained by rotating the curve y = 1 I+ X, 1 <xse about the line x = 28 is…

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Q: Calculate the line integral [F•dr, where F = 3x°yi + x'j in two cases for C1 and C2. These two…

A: The given vector is F=3x2yi+x3j Here we use Green's theorem. So the Green's theorem is…

Q: Find the work done by F(x, y) = (x, Y) over the curve r(t) = (e' cost, e' sin t) (x² + y?)3/2 from…

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Q: 11. Find the equation of the curve whose slope is "m" that passes through a given point "(x,y)".…

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Q: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

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Q: Evaluate y = 4x 2 = [{(x² + 2y)dx + xy. dy} from 0(0, 0)to B(2, 4) along the curve

A: Given the integral is :                                  We have to evaluate the integral from…

Q: Find extrenhum of one of the following function 1. 2(a, y) = sin2(x- 0.5) + artg (y- 0.5) rE (-1,1],…

A: Let us find the Extremum of the given function in the next steps.

Q: Integrate f(r, y, z) = for 0 <t< V3. + y² over the curve r(t) = [cos(t) +t sin(t), sin(t) – t…

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Q: Find a differential operator that annihilates 4e2" cos 3x + 3x²e5.

A: Let L be the differential differential operator that annihilates 4e2xcos3x+3x2e5x. Find L.

Q: F. dr where F = yzi + xzj +xyk and C is the curve x = t, y = 2t², z = –2t² with 0<t < 1.

A: Given F=yzi+xzj+xyk and r=ti+2t2j-2t2k Now the vector field along the curve can be given by…

Q: 1. Show that the field F = (x + cos a)i+ (K +4 – y sin y)j + (2³ + K – 9)k is conservative and find…

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Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

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Q: キIND THE SOLUTIONS to THE DEFF ERENTIAL EQUATI ON y'= x? tyZ %3D メY

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Q: Evaluate the integral с by finding potential function. +2) ax + (x² + 3xy² + 2y)ay along any path…

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Q: 11. Integrate the function. y? dy (49 – y²) 7y y + C V49 – y2 – sin y+C -1 - V49 - y2 | O A. O B.…

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Q: 1. Use the differential df to approximate the change in the value of f(x,y) from the point (1,0) to…

A: We will be using definition.

Q: EX 3! Show that F (x₁y) = (2xy - 3) + " + (2y + x² ) 5* is conservative and find a potential of it..

A: Use the partial derivative for finding the potential function