Let D be the triangular region in the uv-plane with vertices (0, 1), (4, 1), (1, 3) and let G(u, v) = (u − v, 2v). Sketch D in the uv-plane and G(D) in the xy-plane. Find the area of G(D) by using Jac(G)

Q: sketch the region described by the followingspherical coordinates in three-dimensional space. 0 ≤ρ ≤…

A: Given: The region bounded by 0 ≤ρ ≤ 1, π/2 ≤ f ≤ π, 0 ≤ θ ≤ π.

Q: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: Use Green's Theorem to evaluate the line integral. 3x2eY dx + eY dy C: boundary of the region lying…

A: GREEN'S THEOREM:

Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

A:

Q: Let D be the trapezoidal region in the xy-plane bounded by the graphs of x = 0, y = 1, y = x and y =…

A: Explanation of the answer is as follows

Q: a) Evaluate [(2x- y' )dA over triangular region R enclosed between the lines y = -x +1, y = x+1 and…

A: Given integral is ∫∫R2x-y2dA, where R is the triangular region R enclosed between the lines y=-x+1,…

Q: Determine the area that lies under f (x,y) = 9x² + 4xy + 4 and above the rectangle given by [-1,1] ×…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: (c) Use Green's Theorem to evaluate (3xydx+ 2xy dy, where C is a counterclockwise oriented…

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Q: Calculate the line integral fe F. dr, where F = (ry, x² + y² + z², yz), and C is the boundary of the…

A: Given F→=xy,x2+y2+z2,yz and C is the boundary of the parallelogram with vertices…

Q: Use Stoke's theorem to evaluate the integral xydx +2x 'dy-&r 'zdz where C is the boundary of the…

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Q: Given the curve y = x´ and the line y =2- x Find the ordinate of the centroid of the region bounded…

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Q: integrate ƒ over the given region. ƒ(u, y) = y - sqrt(u) over the triangular region cut from the…

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Q: - The region bounded by y = 2 -x, y = 0, x = 1, x = 2 is rotated about the x axis. 197/12

A: volume generated by revolution of the solid is 19π12 detailed solution with explanation is given…

Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: (z+ y – 1) cos D

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Q: Find the area of the surface. The portion of the plane z = 6 - 3x – 2y in the first octant

A: We need to find the area of the portion of the plane z=6-3x-2y in the first octant. Let f(x, y) =…

Q: Let D be the region in xy-plane enclosed by the Trapezoid with vertices at the points (1, 1) , (7 ,…

A: We need to use double integral across given trapezium

Q: Evaluate (y + Vx) dA, where R is the triangular region with vertices (0, 0), (1,0), and (0, 1). R

A: The solution starts from step 2. The information presented below will be helpful to understand the…

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: Find the area of the surface. The part of the cylinder y2 + z2 = 9that lies above the rectangle…

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Q: Evaluate the double integral. I1, 7y? dA, D is the triangular region with vertices (0, 1), (1, 2),…

A: We need to find  double integral , ∫∫D7y2dA  , where D is the triangular region with vertices (0 ,…

Q: 4) Find the centroid of the plane region bounded by x² + y² = 25 and x² + (y – 6)² = 13.

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Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

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Q: Find the centroid (, j) of the region that is contained in the right-half plane {(x,y) | x > 0}, and…

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Q: 3) Find the centroid of the plane region bounded by y = (x – 2)² and 2x – y = -4.

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Q: A region R consists of a square bounded by the lines x = −7, x = 7, y = 0, and y = −14and a half…

A: Draw the region R as follows.

Q: A. Find the area of the plane region bounded by the given curves 1. у%3Dх, у %3D 2х, and x + у %3D 6

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Q: 4) Find the centroid of the plane region bounded by x2 + y? = 25 and x2 + (y – 6)² = 13.

A:

Q: Find the area of the band cut from the paraboloid x² + y² – z = 0 by the planes z = 2 and z = 6.…

A: Given equation is, x2+y2 = z Band cut from the given paraboloid by the planes z = 2; z = 6 Area of…

Q: Evaluate the circulation of G = ryi + zj + 2yk around a square of side 7. centered at the origin,…

A: Given  G=xyi+zj+2yk around a square of side 7

Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: 2. Sketch the two dimensional planar region R = {(x, y) | 0 <x < 2, x² < y < 2x}.

A: Solution Given Seetch the two dimensional planar region R={(x,y)|0≤x≤2,x2≤y2x}

Q: Evaluate the double integral I2 = || y'dzdy T where T is a triangle with vertices (-4, 0), (0, 1),…

A:

Q: b) A solid G is bounded by the planes y + z = 4, z = 0, y = 0 and y = 4 – x2. Evaluate dV 4 – Y G

A: Given that  A solid bounded by the planes of y+z=4,z=0,y=0 and y=4-x^2  To evaluate the integral

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 - and 2r + y…

A: For any triangle that will lie between two planes, one point has to lie on a plane and the other two…

Q: Find the area of the part of the plane defined by 3z + 2y + z 12 that lies in the first octant.

A: Given equation of plane :  3x+2y+z= 12

Q: Evaluate the circulation of Gayi + zj+5yk around a square of side 9, centered at the origin, lying…

A: Solution :

Q: Let M be the region bounded by the parabola y = x² and the line y = x +2. %3D 6. y = r + 2 5. 4.…

A: Consider the given information and diagram: Let y=x2 and the line is y=x+2.

Q: Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

A: The given plane is z=3x+5y+3. Differentiate partially with respect to x, y respectively to obtain…

Q: Find the area of the finite part of the paraboloid  y = x2 + z2 cut off by the plane y = 4.

A: To find the area of the finite paraboloid y=x2+z2 cutt off by the plane

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 and 2r + y -…

A: The equations of the two planes are: 3x-6y-2z=152x+y-2z=5 As, 5,0,0 satisfies the equation of plane…

Q: Compute s F=

A:

Q: Evaluate |[A.ndS where A = 2xyi+yzj+xzk and S is the surface of the region bounded by x = 0, y = 0,…

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Q: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: Calculate (x+ y)dA, where Ris a triangular region with vertices (0,0), (3,0) and (3,3).

A:

Q: Let R denote the region in the first quadrant of the ry-plane that is bounded by y = /4 – x², y =…

A: The definite Integral for given problem with proper reasoning has been formulated in step 2.

Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…