What is the center of gravity of the solid formed when the plane region bounded by y = x, y = 2x, and x + y = 6 is revolved about the y-axis ? O (13/5,0) O (3/5,0) 2 O (0, 13/5) O (0,3/5) O NA

Q: Evaluate I = , dx dy where R is the region that lies inside the circle x2 + (y – 2)2= 4 and outside…

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

Q: 3.Obtain the centroid of the solid formed of the area bounded in the first quadrant by y = 2x7, the…

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Q: . Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = y², xy-plane and…

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Q: Find the equation that solves the area of the surface obtained by rotating the curve x = (y² + 2)% ,…

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Q: 2. Find the centroid of the area bounded by y = 4x – x² and the x axis. a. Sketch the area and find…

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Q: 2. Find || F dS where is the outer surface of the solid x²+y² +z? = 4 hemisphere - z20 oriented…

A: Using divergence theorem solve the integral:

Q: Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: The line joining P1,0 and Q0,1 is     x-11-0=y-00-1=t(say)⇒x=t+1,y=-t⇒dx=dt,dy=-dt

Q: (c) Evaluate dx dy 1– x² – y² where R is the right half-disk of radius % and centered at (0, % ).

A: R: (x-0)2+(y-1/2)2=1/4, x≥0 x2+(y-1/2)2=1/4

Q: (2x + 3y - 1) dx + (4x +6y + 2) dy = 0 Give the: a. homogeneity b. degree c. reducible…

A: Given : 2x+3y-1dx+4x+6y+2dy=0 To check homogeneity and find degree and reducible homogeneous form.

Q: The histogram Height for 355 students. Frequency 40- 30- 20- 10-

A: A histogram is a visual depiction of how values in a set of data are distributed. A histogram is…

Q: Use Cartesian coordinates to evaluate [[[ ²² y² dv D where D is the tetrahedron in the first octant…

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Q: O Evaluate 2 fff ( x + y ) dv G where G is a solid took thes to sicle bounded by the parabolic…

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Q: Evaluate SS x² y4 dx dy D 1 where D is the region bounded by the hyperbolas xy-2, xyalk parabolas y²…

A: We have to Evaluate the integral  ∬Dx2y-4dxdy where D is the region bounded by the hyperbolas xy=2,…

Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: Use cylindrical coordinates to calculate Jw J(x, y, z) dv for f(x, y, z) = x, (Use symbolic notation…

A: To evaluate ∫∫∫Wfx,y,zdV, Where fx,y,z=x  & W is the region bounded by x2+y2≤9,x≥0,y≥0…

Q: Which of the following represents the equation z=x2+y2 in cylindrical coordinates?     r2=z…

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Q: (a) y² + ² = 4 that lies inside the cylinder x² + y² = 3. Find the area of the surface S, which is…

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Q: The region enclosed by y=2Vx and y=6 is revolved about the x-axis. The volume of the solid generated…

A: The given curves are: y=2x, y=6

Q: The remainder upon the division of x98 +4 by x - 2 in z, is: 6. None

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Q: 3. An R region of the XY plane is shown below: y = -8/a 2y +z = 4 y=-1/2 2y +a= -1 R If A is denoted…

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Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

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Q: 2. Evaluate O (2y + In(5x² +3)) dx + (10x 3) dy along the boundary of the elliptic- region 4. y? 1…

A: Introduction: Green's theorem is very efficient in calculating line integral. When the line intgeral…

Q: Evaluate || F.ndS F = xi + yj+(z² –1)k if and o is the curved surface of the cylinder y = \4-x? from…

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Q: (a) Use a Green theorem to evaluate (y¹ - 2y)dx - (6x - 4xy³). dy where c is the boundary of the…

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Q: Exer.) Express and evaluate the integral (x+y) dv E as an iterated integral for the given solid…

A: Given:

Q: Let f(x, y, z) = In (x² + y + z?). The level surface f (x, y, z) = In 4 is a: Elliptical cone around…

A: Given  f (x,y,z) = ln( x2+ y+z2),To find : level surface f= ln4

Q: Let o(r, y, 2) = x2 + (y/2)2 + 22. Find the point on the ellipsoid o = 1 closest to (1, 1, -1).

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Q: The "R" region is bounded by the following parametric equation: x = a(t – sen(t)), y = a(1 – cos(t))…

A: Please check step 2 for the solution.!

Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

Q: w √√x² + y² dv, where W is the region between the half cone zwx+yeyers, and ircular paraboloid z=2-…

A: A volume integral is given over the region W. The aim is to find the volume integral for the given…