Find the average haight of the Paraboloid z- xry* over the square osx <2, osd<2

Q: Find the surface area of the part of the paraboloid z = 9 – 2.x - 2y that lies above the %3D

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Q: Calculate the double integral Sle (x² + 2y) dA, where R is the triangular region with vertices 8/3…

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Q: Evaluate the double integral 8xy dA, where D is the triangular region with vertices (0, 0), (1, 2),…

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Q: The surface area of the part of z = 2 + V4 – x² – y² that lies inside the paraboloid z x² + y² is

A: This is a problem of vector calculus.

Q: Find the y coordinate of the centroid of the region shaded in the following diagram. 9 in. -27 in.

A: Here the figure has drawn for our convenience.  To find the centroid, the rectangle indicated in x…

Q: Let C be the positively oriented square with vertices (0,0) (2,0), (2,2), (0,2) Use Green's Theorem…

A: Consider the provider question,

Q: Show that the area of that portion of the surface of the paraboloid x² + y² = 4z included between…

A: Here we need to find area between given plane and x*x + y*y = 4z

Q: What is the y=x^2 - 4 and O 1/4 O 1/2 01 03/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

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Q: EXAMPLE 2 Find the area of the part of the paraboloid z = x + y' that lies under the plane

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Q: Find the area of the portion of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4.

A: Given that ,  paraboloid   z=x2+y2 cylinder        x2+y2=4

Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

Q: ind the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above the…

A: Using the double integral formula.

Q: Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices…

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Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

A: Formula: The surface area of the function z=fx, y over the region D is: SA=∫∫D1+zx2+zy2 dA The given…

Q: The solid bounded by the paraboloids 2= - 8+z²+ y² and z -3-32²-3y² has volume:

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Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 +…

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Q: | Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2). (0, 2). Use Green's…

A: greens theorem

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

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Q: Find the centroid of the portion of the sphere x2 + y2 + z2 = a2 that lies in the first octant.

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Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

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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: Evaluate the double integral || 8xy dA, where D is the triangular region with vertices (0, 0), (1,…

A: Given data: The first vertex is O=(0, 0). The second vertex is B=(1, 2). The third vertex is A=(0,…

Q: Evaluate ∫∫∫E √x2 + z2dV, where E is the region bounded by the paraboloid y = x2 + z2 and the plane…

A: Given, y=x2+z2 ⇒z2=y-x2z=±y-x2 Therefore the limit of z is -y-x2≤z≤y-x2 On drawing the graph in the…

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

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Q: 4. A 5m x 5cm is cut from a corner of 20cm x 30cm. cardboard, find the centroid from the longest…

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Q: 4. Locate the centroid (x, y)of the following composite areas:

A: The centroid of rectangle is given by x2,y2 where x, y are the length and width respectively. The…

Q: The shape of a redwood tree (without any branches) can be modeled by an upside down paraboloid, f(x,…

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Q: Let T be the triangular region with vertices (-1,0), (0,1), and (1,0). Use an iterated integral to…

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Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: Evaluate the double integral ∬D2xydA,∬D2xydA, where DD is the triangular region with vertices…

A: Evaluate the double integral ∬D 2xydA where D is the triangular region with vertices (0,0), (1,2),…

Q: Evaluate || F-n dS where S is the cylinder (including the disk on the bottom) x² + y² =1 for 0<z<1…

A: First, we plot the given surfaces.Cylinder : x2+y2=1; 0≤z≤1Paraboloid : 3x2+3y2+z = 4; 1≤z≤4.

Q: Find the average height of the paraboloid z = x2 + y2 over the square 0&lt;= x &lt;= 2, 0…

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Q: Evaluate the double integral || 8xydA, where Dis the triangular region with vertices (0,0), (1,2),…

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Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

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Q: ) Evaluate the double integral | 4xy dA, D where D is the triangular region with vertices (0,0),…

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Q: Let D be the solid region bounded above by z = -5x² +y? and below by z =-5. Then the projection of D…

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Q: Find the area of the portion of the paraboloid x = 4 - y2 - z2 that lies above the ring 1&lt;=y2 +…

A: Given surface is  The required surface area is given by where

Q: Let D be the solid region bounded above by z = -3/x² + y² and below by z = -3. Then the projection…

A: Given Region D is bounded  above by cone  Z=-x2+y2and bounded the  below by  plane z=-3

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 – x2 + 2 and above…

A: To find the volume of the solid that lies under the hyperbolic paraboloid  z=3y2-x2+2 and above the…

Q: . Set up the triple integral fSSp r+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

A: The equation of tetrahedron with intercepts (a,0,0), (0,b,0) and (0,0,c) is given by: Given…

Q: {[]-0=y<{u{[;} In R², let S = Describe (or sketch) the convex hull of S.

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Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: Q1- Determine the coordinates of the centroid of the area.: (1, 1) y= x,

A: The given problem is to find the centroid of the given shaded area of the region formed by given…

Q: Compute s F=

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Q: Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 1

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Q: Q1- Determine the coordinates of the centroid of the area.: (1, 1)

A: We need to find the x coordinate and y coordinate of the shaded region which is bounded by two…

Q: Evaluate the double integral. 6y? dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

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Q: Find the centroid (, j) of the triangle with vertices at (0, 0), (8, 0), and (0, 9). x=

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