2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y = a

Q: The area of the region bounded by the curves 2y2 +2 and z 2y+2 is 2. 3 5 -1 -2 16 17 (A) 3 (B) 3 13…

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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: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

A: 25.   Given that:   The plane y+z=2 and the cylinder x=4-y^2. The region in the first octant bounded…

Q: Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x =…

A: Here, the surface is in the first octant. Therefore, the integration is

Q: Evaluate (x + 2y) dA, where R is the region bounded by the parabolas y = 2x² and y = 1 + r?.

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Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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Q: Use Green's Theorem to evaluate: So F.ñ ds C where F = (Vx + 6y, 2x + 6y) and C is the boundary of…

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Q: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: 28. Show that the circulation of F(x, y, z) = (x², y², z(x² + y²)) around any curve C on the surface…

A: Given figure Stoke's Theorem Here take single integral over closed path C and double integral over…

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: Consider the area of the part of the plane z=ax+by+c that projects onto some region D in the…

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Q: Find the area of the plane x+2y+2z=2 cut out by the cylinder x^2+ y^2=4

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Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

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Q: H.W where or is the selid bounded the Sur faces

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Q: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

Q: Find the area of the surface defined by x + y + z = 1, x2 + 8y2 s 1.

A: Given,            x+y+z=1,     x2+8y2≤1

Q: Evaluate the line integral xyld x + (x²+y)dy] +. where c is the saruare farmed by the lines

A: Let us consider a line integral ∫CP dx+Qdy then it can be written as  ∫D∫∂Q∂x-∂P∂y dA  Where, P and…

Q: Sketch the region enclosed by the given curves. x = 9y2, x = 28 + 2y2 y y 21 35 30 1 25 20 5 10 15…

A: x=9y2,  x=28+2y2 The region is,

Q: 2 Find the surface area of the portion of the cone x² + y² = 2² above the region inside the…

A: we have to find the surface area of the portion of the cone x2+y2=z2 above the region inside 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 vohume fome above ZVy-xLy, below Z0(xy plane) inside xy/ 3.

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Q: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

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Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: Verify Stoke 's Theorem for F = (x² +y – 4) î + 3 xyj + (2 xz + z²) k over the surface of hemisphere…

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Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

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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: 135 2. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: s. u.) 4

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Q: Find the volume of the Intersection curve C C Projection of C on ay-plane

A: Given: Given paraboloids are z=x2+y2 and z=8-x2-y2 We want to find the volume bounded by the…

Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

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Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

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Q: 13. Find the area of the surface given by z-f(x,y)%3Dxy ov (x,y):x² +y² <100). R:

A: We have to find the area of surface according to the given information

Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: An integral expression for the area of the surface generated by rotating the line segment joining…

A: Given that: Points are- (3,1) , (6, 2)

Q: Compute ,F · dS for F = (xy, 5y,0), S being the cone z² = x + y²,x² + y? 0, with the normal %3D…

A: The vector field is F=⟨xy, 5y, 0⟩ and the parametric equation of the cone is  Rr, θ=rcosθ, rsinθ, r…

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: E is the region behind the surface y = 4 – x² that is in front of the region in the xy-plane bounded…

A: Given integral: ∫∬E18x dV Given that E is the region behind the surface y=4-x2 that is in front of…

Q: 7. D is bounded by the surface (a2 + y² + z²)² = a²(x² + y? – z²). %3D

A: Sol

Q: Compute s F=

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Q: b. Draw the image of the W-plane into which the region bounded by the straight lines in the Z-plane…

A: The solution is given below

Q: Find the area of the surface f(x,y)= x² + 3y over the triangular domain bounded by the x-axis, the…

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Q: Let R denote the region in the first quadrant of the ry-plane that is bounded by y = V4 - 1², y =…

A: Curves in the x-y plane are  y=4-x2,y=2x &amp;y=0 Now, when you see the area enclosed under these…

Q: Find the surface area of the portion of the cone z = x2 + y2 in between the planes z = 3 and z = 4.

A: The area of the surface z=fx,y above a region R of the xy-plane is given as follows.…

Q: Calculate fSp(3x + 2y) dA where D is the region in the first quadrant that is inside the circle x2 +…

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

Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…