Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise. 3xy dx + 2xy dy, where Cis the rectangle bounded by x = - 1,x = 1,y = 3, and y = 5. 3xy dx + 2xy dy :

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A: Consider the function  f(x)=3x

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A: T(x,y,z)=200e-x2-14y2-19z2 The gradient of the temperature is: ∇T (x, y, z) = −200〈2x-x2-14y2-19z2 ,…

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A: 0≤ z ≤ 81-x2-y2z=0x2+y2=920≤y≤81-x20≤x≤9

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A: Absolute maximum and minimum from graph

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A: answer is in next step

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A: Given query is to find the value of the integral.

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A: Given problem:- Find dy/dt for the parametric curve c(t) = (t-1 - 5t, 4t3) at the point t = −2.

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A: According to guidelines  we must answer only three of multipart questions. Please resubmit the…

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A: The objective of the question is evaluate the area of the given bounded region.

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Q: Solve the given differential equation by separation of variables. dy ху + бу — х— 6 dx ху — 5у + х —…

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Q: (6) (a) For each of the following differential equatons: • Determine the order of the differential…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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A: Given problem:- Solve the following differential equation y'' -y=xe-x

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A: The slope of tangent to a curve y=f(x) at a point x=a is given by f'(a)

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A: Use the derivative for finding the answer.