need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first octant that is between the xy-plane and the surface x2 + 2x + y − z = 4

Q: Evaluate the surface integral. ) ر م(ل 2) ds S is the part of the cylinder x² + y2 = 16 that lies…

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Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

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Q: Find the surface area of the portion of the paraboloid z = 9- r - y? between the cylinders r?+ y? =…

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Q: Find the volume of the region bounded above by the sphere x² + y² + z² = 2b?and below by the…

A: To determine: The volume of the region bounded above by the sphere x2 + y2 + z2 = 2 b2below by the…

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z=3y^(2)−x^(2)+4 and above…

A: The volume of the solid is determined by

Q: Find the surface area when C {(x, y): 0 ≤ x ≤ 2; y = 1 is revolved about the y-axis.

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Q: Consider the solid region E inside the sphere x² + y² + z² = 4 and outside the cylinder x² + y² = 1.…

A: This question is based on 3-D geometry.

Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x? + y2 =…

A: Consider the formula for the Surface and the function f(x,y).Calculate fx and fy by partially…

Q: Let S be the part of the hyperbolic paraboloid z = x2- y2 located between the cylinders x2 + y? = 1…

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder a² + y?…

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Q: Evaluate the surface integral |[(x² + y° \dS_where S is the surface of the paraboloid z = x² + y²,…

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Q: Evaluate the surface integral. z + x2y x²y) ds S is the part of the cylinder y² + z2 = 9 that lies…

A: We have to find the surface integral from the given condition

Q: Evaluate the surface integral. dS S is the part of the sphere x2 + y² + z? = 16 that lies inside the…

A: The objective is to find the surface integral  ∫∫Sy2dS  where S is the part of the sphere…

Q: Evaluate the surface integral. z2 S is the part of the paraboloid x = y2 + z² given by 0 sx 5 4 1 V5…

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Q: The area A(E) of the surface E that is the part of the surface z = xy that lies within the cylinder…

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Q: Evaluate the surface integral: S Ssx*y ds Where S is the surface of the paraboloid z = 4 – x2 – y?…

A: To evaluate the given surface integral, use the following formula. ∬SFx,ydS=∬DFx,y1+∂z∂x2+∂z∂y2dxdy

Q: -. Evaluate the surface integral z'/x2 + y?dS, where S is the surface parametrized by Ocoso, y =…

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Q: Evaluate the surface integral. y ds S is the part of the paraboloid y = x² + z² that lies inside the…

A: The projection of S onto the xz-plane is the disk D=x,z: x2+z2≤9. We have to calculate the surface…

Q: Evaluate the surface integral  ffR(x+y)dS where σ is the portion of the plane z = 6 − 2x − 3y in the…

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Q: Evaluate , x*+2y* D 2x++8y++2z+ dV, where D is the region enclosed by the spherical surface x2 + y?…

A: Given: To evaluate ∫∫∫D x4 + 2y42x4  + 8y4 + 2z4 dV  Where D is the region enclosed by the spherical…

Q: Q2 (a) Find the volume under the surface z = 3x³ + 3x?y and over the rectangle R = {(x, y):1 < x <…

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

A: Please see the explanation below

Q: Find the surface area of the portion of the cone z? = 4x? + 4y? that is above the region in the…

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Q: Evaluate the surface integral || x2 z2 dS, where S is the part of the cone z2 = x² + y?, S that lies…

A: Here we solve the given problem of calculus.

Q: (a) Evaluate the following surface integral yex²+z² dS, where o is the portion of the surface of the…

A: Given the integral ∬σyex2+z2dS we have evaluate the given surface integral where σ is the portion of…

Q: nd the volume of the solid bounded by the paraboloid z = 32 – x² – y², the cylinder r² + y? = 16 and…

A: The solution are next step

Q: Show that the volume common to the surfaces 2 p2+z=4ax and x+y?=2ax is (3r+8)*. 3

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Q: Consider the paraboloid z = 1- ² – y?. Find the volume of the region between this surface and the ry…

A: According to the problem,. we have

Q: 1. Consider the surface which is the part of the sphere r? + y? + 2? = 4 that lies above the cone z…

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Q: 5. Find the volume under the paraboloid = -a? – y?, and above the cone z = - p² + y?.

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Q: 2. Find the area of the surface generated by revolving the given curve about the y -axis. (a)…

A: Given b x=y3, 0≤y≤2c x=9-y2, -2≤y≤2

Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: Find the volume of the solid that lies under the surface z = 4x + 5y + 20 and above the region D in…

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Q: Determine the resulting surface area when the curve y = x is rotated about the y-axis in the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: The volume of the solid generated by the curve y = e, between r = 2 and a = 7 about %3D %3D the x…

A: Given : y = e-x

Q: Find the area of the upper portion of the cylinder x² + z? = 1 that lies between the planes x = ±1/2…

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Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

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Q: tind the volume Of the solid bounded below the Sphere t+Z=1, above the ay-plane Cre z >o and to the…

A: To find the volume of the solid between the sphere x2+y2+z2=1, above the xy-plane and to the right…

Q: Find the surface area of the portion S of the cone z2 = x? + y², where z > 0, contained within the…

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Q: (a) Compute the surface integral || xy dS, where S is the quarter cylinder x? + y? = 1; x, y > 0…

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Q: Q2 (a) Find the volume under the surface z = 3x³ + 3x?y and over the rectangle R = {(x, y): 1 < x <…

A: Volume of the surface and surface  area using double integral

Q: 1. Find the surface area of the cone z = √x² + y² that lies between the plane y = x and the cylinder…

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Q: The volume of the solid generated by revolving the region between the parabola xr=y2+1 and the line…

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Q: Evaluate the surface integral (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: We need to calculate:∬S4x2+3ydS over the surface S,which is the part of plane 2x+5y+z=48, inside the…

Q: Let S be the part of the cylindrical surface x2 + y2 = 4 limited by the plans z = 0 and z = y + 2.…

A: Let S be the part of cylindrical surface x2+y2=4, limited by z=0 and z=y+2 The formula to find the…

Q: Evaluate the surface integral. SS, xz ds, S is the part of the plane 2x + 2y + z = 4 which is in the…

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Q: Find the surface area of the portion of the semi cone z = x2 + y? that lies between the planes z = 6…

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Q: Evaluate the surface integral. (x²z. y?z) as x2z + S is the hemisphere x2 + y2 + z² = 4, z 2 0

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