5. Calculate the following integrals D 12A, where D is the triangular region with vertices (0,0), (1, 1), and (0, 1). xdA where D is the region in the first quadrant between the circles x2 + y² = 1 and x² + y² = 2. (b) fa D

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A: We have to find ∬Rdxdy where R is the region that lies inside the circle x2+y-22=4 and outside the…

Q: 2. Find the area of the plane figure bounded by the curves. Plot the graphs of the given functions,…

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Q: Determine the surface area of the plane 2x+y + 2z = 16 cut off by x = 0, y = 0 and x² + y² = 64.

A: Area of surface given by z = f(x,y) A=∫∫Dfx2+fy2+1dA  where (x,y) is a point from the region D in…

Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x²…

A: Solution: If surface 's' has equation of form z= f(x,y) and if 'f' has continous partial…

Q: (r – 1)² = –4(y – 1) y 9a² + 16(y – 2)² = 144 3 -2 1 0 2 5 -2 -3

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Q: 10. Find all the planar and hyperbolic points on the surface o(u, v) = u-3uv².

A: A point on a surface is said to be a hyperbolic point if the Gaussian curvature at p,i.e., κp<0.…

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: 2. Let D be the parallelogram bounded by the lines x+3y = 5, –x + y = 3, –x + y = 2, and x + 3y = 0.…

A: Let us consider the integral I=∫∫Df(x,y) dydx where D is the region in xy-coordinate  To make the…

Q: ). Find the centroid of the first quadrant area bounded by the parabola y = x2 and the line y = x.…

A: According to the guidelines answer of first question can be given, for other please ask in a…

Q: Use traces to graph and name the surface

A: The given surface is: x24-y29+z216=1...(1)

Q: 6. Find the area of the part of the surface z = x²-y², which lies in the first octant that is inside…

A: The solution is given by

Q: where Dx = X₁-X₂ and Dy = |Y₁ — Y2]. Assume that the two locations are independent and uniformly…

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Q: J₁ R - x + 3y = 0, x + 3y Round your answer to 4 decimal places. Find - x + 3y -dA, where R is the…

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Q: 4. Find the surface area of the part of the sphere x² + y² + z² = 1 above the plane z = 1/√2.

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Q: 1. Calculate y³ $ £ (-2² - sinz) dz + ( + v) ds. + dx dy, 3 3 where C is the circle of radius 1…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: We have to use Langrages Multipliers Method to find the minimum distance from (0,c,0) to a point on…

Q: dz 5. Evaluate the integral where C is the circle (a) |z| = 1, (b) |z+3| = 2, (c) |z – 3| = 2. 23(z…

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Q: 4. Evaluate ff(2x- y²)dA over the triangular region Renclosed between the lines y =-x+1, y=x+1, and…

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Q: Find the exact area of the surface. :=+2y,0sxS1,0sys2 Oa 2+ n(4) Ob. Sin(3) 4. Oc3-In(5) Od 5…

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Q: Let C consist of the part of the circle r +y = 4 from (2,0) to (0,2), Followed by the line segments…

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