4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C is the boundary of the square with vertices ±(2,2) and ±(2, -2). ( do not evaluate the integral)

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

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Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

A:

Q: What is dyldx at the point (1,2) of xy^2 + 2xy 8 ?

A: The given equation is: xy2+2xy=8...(1)

Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

A:

Q: 2(x + y)i + sin(y) 3. Find the line integral of Faround the perimeter of the rectangle with corners…

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Q: Sketch the surface x = 2y2 +3z2

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Q: Evaluate This Integral if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to…

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Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x…

A: In the given question we have to find the double integral of paraboloid z=x2-y2 ovet the triangle…

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Q: Find div F and curl F if F(x, y, z) = xªi – 6j + yzk. div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = xzºi + 6y²x²j + 6z²yk. div F= curl F=

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Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the

A: Introduction: A line integral in calculus is an integral where the function being integrated is…