Evaluate the integral r+y e-- dxdy R where R is the trapezoidal region with vertices (1, 0), (2,0), (0, –2) and (0, –1). Consider using the following change of variables: u = x + y, v = x – y.

Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

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A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices…

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Q: Evaluate exp{}dA where R is the region in the ry-plane bounded by the trapezoid with vertices (0,…

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle…

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Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Theorem to…

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Q: Use the Jacobian of a coordinate transformation to find the area of the parallelogram bounded by the…

A: We use the following transformation to find the area of the parallelogram bounded by the lines y =…

Q: Find the points on the plane r - y = 2 – z closest to the point (1, 1, 1).

A: We will find the closest point on the given plane as following.