e-(z²+y²+z²) dV. x² + y² + z² where E is the region bounded by the spheres x? + y² + z² 1 and x? + y? + z2 = 16.

Q: SI (1 0x°y - 6)ixdy where S is the region bounded by -2y? and Evaluate X = x = y'.

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Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: (B) Integrate g(x,y,z)=x+y(x+2z) over the surface area of the region cut from plane x+2y+2z=5 by the…

A: What is Surface Integral: Surface integral is an iterated integration that is performed over a…

Q: 1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and…

A: To find the volume of the prism described we just need to evaluate the given double integral…

Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

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Q: Let R be the region bounded by y = 6.5 – x, the x axis and the y axis. 6 4 3 2 1 The solid obtained…

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Q: D Evaluate xy dady where D is Hie region bounded x=0, y=0, and x+y= ! by

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Q: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: Find the area of the plane region, 0≤x≤ π²-4 S.U. 4 1.111 s.u. 1 s.u. 2 S.U. bounded by y=sin X. X =…

A: This question can be solved using the concept of area under curves.

Q: (b) Calculate the volume of the tetrahedron in the first octant bounded by the plane x + 2y + 3z = Q…

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Q: (d) I dA over the region R bounded by r² + y² = 25, y = V3r, and I= 0.

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Q: Evaluate the moment M, and M,y of the region bounded by y = 2x+ 1, x + y = 7 and x = 8.

A: fx = y = 2x+1gx= y = 7-x      Mx=12∫LLULfx2-gx2dx               Moment about x-axisMy=∫LLULxfx-gxdx…

Q: a)Calculate the integral [D zdV on the D region bounded by the 6 = x2 + y2 paraboloid from the…

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Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: Sketch the region D = {(x, y, z): x2 + y2 ≤ 4, 0 ≤ z ≤ 4}.

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Q: Calculate ff F.n dS where F x'yzi + 2xj + y?k in the solid region S bounded by the parabolic tube z…

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Q: Evaluate I/| V x2 + y² dV, where E is the region that lies inside the cylinder x2 + y? = 16 and…

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Q: 4. Find the volume of the solid under the surface f(x, y) = xy and above the triangular region in…

A: .

Q: Q5: Find the volume of the solid bounded by surfaces z = /9- x2 - y2, and z = /25 – x2 - y² and the…

A: Given solid is bounded by Z = 9-x2-y2 and Z = 25-x2-y2 and x2+y2-z2 = 0

Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: Q3 Verify Green's theorem in plane for (x² - 2xy) dx + (x²y + 3)dy where c is the boundary of the…

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Q: 2- Find D xyz dV where D is the region with -1 ≤x≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2.

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Q: Evaluate f S Sp(2+ e(=²+v²+z*)*/²) dV, where B = {(x, y, z) | x² + y² + z² < 9} Describe the region…

A: Consider the provided question, (2) (a)

Q: Find the area of the region described in the following exercise a. The region bounded by y=4x+4,…

A: Since you have asked multiple questions in a single request, we would be answering only first…

Q: (b) Let D be the region of R3 which lies outside the cylinder x² + y2-1, inside- the sphere x² + y²…

A: let D be the region of R3 which lies outside the cylinder x2+y2=1, inside the sphere x2+y2+z2=4 and…

Q: Evaluate . (y² z)dV where E be the region in the first octant E bounded by the planes x = z, x + z =…

A:

Q: Find the volume.

A: Consider the provided question,

Q: Eraluate: 1. JJR e-(n^²+yv) the eincles of padii 1& 2 dady, R is the region of between.

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

Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

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Q: graph of the region of integration. • 3x/4 : | f(r,0) r dr do ? v 1. A в 7/4 2x ? v 2. 2 3x/4 ? v 3.…

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Q: C. Find the volume of the solid obtained by rotating the region bounded by y = -10 + 6x-x², x = 1…

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Q: ds k(4nr). dt --Select-- %3D volume dV k dt surface are ds - ). dt dV dt dV = k(4tr²). dt

A: Given evaporation rate proportional to surface area Use formula of volume and surface area to find

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

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Q: (c) Find II zdV where E is the region bounded by the cylinder y² + z² = 9 and the planes E x = 0, y…

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Q: A region R is bounded by the graphs of y=0.5 Vx and y=0.5x. Find the moments Mx and My of R about…

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Q: | 5z2 dV , where E is Evaluate E the region bounded below by the cone z = Vx2 + y² and above by the…

A: Given: ∫∫∫E5z2dvz=x2+y2x2+y2+z2=1

Q: Verify Green's theorem in the plane for S(3x² -8y )dx +(4y-6xy)dy, Where C is the boundary of the…

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Q: Evaluate /VT² + y² dV_where E is the region that lies inside the cylinder E x² + y? = 4 and between…

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Q: the region bounded by the cylinder x2+ y2 = 4 10TT and the planes Z = 0 and X+Z =5 %3D 20T1 O 50TT…

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Q: Evaluate z dV where E is the region bounded between the spheres x² + y² + z² = 1 and x² + y? + z° 4…

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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: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…

Q: Verify Green's theorem in a plane | (xy +x²)dx + x² dy, where C is the boundary of the region formed…

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Q: Q5: Find the volume of the solid bounded by surfaces z = /9 - x2 - y2 , and z = /25 - x2 - y? and…

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Q: B. Find the volume of the indicated solid i) under 2x - 3y + z = 6 and above the rectangle R = =…

A: Let's find volume of solid(V).

Q: 2. The solid in the first octant bounded by the planes x = 0, y = 0, z = 1, z = 2 – y, and the…

A: