Let I = , zdV ,where D is bounded by the planes x = 0, z = 0, x+ y = 2 and the cylinder x2 + z2 = 1 in the first octant, then I = %3D %3D 6.

Q: y dV W

A: Let us consider the triple integral ∫ab∫h(x)g(x)∫p(x,y)q(x,y)f(x,y,z)dzdydx To solve the integral…

Q: The solid E in the first octant of 3-space shown in is bounded by the cylinder z = 1– x² and the…

A: Let's find.

Q: A) Evaluate the triple integral ydV, E = 0, where E is the solid region bounded by the cylinder 4 =…

A: Given

Q: Let S be the solid bounded by the planes z = o and y + z = 3, and the cylinder x2+y2 =2y-

A: answer is in next step

Q: Evaluate J, (2x + y) dV, where V is closed region bounded by the cylinder : = 4 – and the planes 4.…

A: Q. Evaluate ∭V(2x+y)dV, where V is closed region bounded by the cylinder z=4-x2 and the planes x=0,…

Q: Use Green's Theorem to evaluate | F nds, where F = (Va+ 5y, 4x + 5y) %3D C is the boundary of the…

A: We have to evaluate the integral ∫CF→·n→ds, where F→=x+5y,4x+5y. Where C is the boundary of the…

Q: Let D be the trapezoidal region in the xy-plane bounded by the graphs of x = 0, y = 1, y = x and y =…

A: Explanation of the answer is as follows

Q: Use Green's Theorem to evaluate F. nds, where F = (Va + 4y, 2æ + 4y) C is the boundary of the region…

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Q: Let E be the region bounded by the hemisphere x² + y? + (z – 2)² = 4, 2 < z < 4, and the plane %3D z…

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Q: Use Green's Theorem to evaluate F nds, where F = (Va + 6y, 3x + 6y) C is the boundary of the region…

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Q: Consider the surface S: z = 4 - x2 ,bounded by y = −5(x2 - 1) and y = 0, just as it is shown in the…

A: We have to find the area of the surface S, and we will use surface integral to do that.

Q: Evaluate the integral ∭U(x4+2x2y2+y4)dxdydz, where the region U is bounded by the surface x2+y2≤1…

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Q: A solid G is bounded by the paraboloid z = 4 - x? – y?, the cylinder x² + y? = 4 and the plane z =…

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Q: Let I = , zdV ,where D is bounded by the planes x = 0, %3D 6. z 0, x+y = 2 and the cylinder x2 + z2…

A: Given: I=∫∫∫D z dVwhere D is bounded by the planes x=0, z=0, x+y=2 and the cylinder x2+z2=1 in the…

Q: Let D be the closed region in R? bounded by x2 - 2xy + y² + x + y = 0 and Q3. x + y + 2 = 0, as…

A: Given: x2−2xy+y2+x+y=0x+y+2=0

Q: Evaluate /// 203 dV G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Here we have to find range of values for x,y and z and then find triple integral

Q: Let C be the positively oriented square with vertices 0, 1, 1 + i, i. Evaluate using the definition…

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Q: Evaluate the triple integral ///. zdV, where E 4. is bounded by the cylinder y2 + z? = 4 and the…

A: According to the given information, it is required to evaluate the triple integral.

Q: Use Green's Theorem to evaluate C |F.nds, where F = (Va+ 3y, 20 + 3y) C is the boundary of the…

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Q: Let C be the counterclockwise boundary of the region enclosed by the x-axis, the line y = x – 2, and…

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Q: Set up the integral [ s (x, y,z)dV six different ways where E is the solid in the first octant…

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Q: Evaluate the triple integral. sssE (x − y) dV,where E is enclosed by the surfaces z = x2 − 1, z = 1…

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Q: Let R be a region bounded by the four planes a = 0, y = 0, z = 0 and a + y + z = 9. Evaluate SSS 24x…

A: In this question we will use basic of calculus i.e application of integration. We will simply apply…

Q: The value of the integral [[Fnds, where s is the surface of the cube in bounded by x 0, x = 2, у %3D…

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Q: 2. A solid G is bounded by the paraboloid z = 4-²-y², the cylinder x² + y² = 4 and the plane z = 5.…

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Q: Let F(r, y, z) =r²i+y´j+z²k and S the surface of the region bounded by the cylinder r² + y² = 16 and…

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Q: Use Green's Theorem to evaluate |F.n ds, where F (Va + 4y, 2x + 4y) 2x x2 and the x-axis (oriented…

A: Given F→=x+4y,2x+4y We have to find the ∫CF→⋅n→ds, where C is the boundary of the region enclosed by…

Q: Use Green's Theorem to evaluate nds, where F = (Va+ 3y, 2a + 3y) C is the boundary of the region…

A: Given Vector field is  F=x+3y, 2x+3y Comparing with F=P,Q, we get  P = x+3y            and…

Q: Evaluate the triple integral. SIJE3Y dV, where E is bounded by the planes x = 0, y = 0, : = 0, and…

A:

Q: Let D = {(x, y) | 2 <r S 3, , -<0<0}. Sketch the region D, and evaluate the double integral lp -4y…

A: We will use polar coordinates.

Q: Evaluate SSS z²dV, where R is the region given R by above the plane z=O and between the spheres 2. +…

A: A scalar function is a rule that is used to associate a number, or quantity with a particular point…

Q: Evaluate zdV where E is the region under the plane 4x + 2y + z = 4 in the first octant ( E х, у, z >…

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Q: Let D be the trapezoidal region in the xy-plane bounded by the graphs of x = 0, y = 1, y = x and y…

A: Here I am attaching image so that you understand each and every step.

Q: Let E be the region in R³ bounded by the surfaces x² + y² = a², z = 0, and z = h. What does the…

A:

Q: Let F(r, y, z) = r²i+ y²j+ z²k and S the surface of the region bounded by 5. the cylinder 1? + y² =…

A: Divergence theorem

Q: Calculate ( (2x + y) dV , where V is a closed space bounded by the cylinder z = 4 – x? and the…

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Q: Let E be the region bounded by z=4 - 2r - 2y and z = 2. Evaluate the following triple integral: 12zy…

A: The given region is bounded by: z=4-2x2-2y2 ,   z=2

Q: Compute the contour integral dz, where l'is the contour of the perimeter of the square with vertices…

A: We will do it  by dividing r into 4 paths.

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 solid G is bounded by the paraboloid z = 4 – x2 – y?, the cylinder x2 + y? = 4 and the plane z =…

A:

Q: Let W be the region that is cut aut from x't v<4 by the pora blae id Rs X'ty ond the plane =10.…

A:

Q: 1) Evaluate the triple integral SS, f(x,y,z)dv : B) f(x,y,z) = 3y² – 2z , Q is the tetrahedron…

A: given f(x,y,z) = 3y2-2z, Q=3x+2y-z=6 The region bounded by the equation Q is a tetrahedron cutting…

Q: Use Green's Theorem to evaluate rids, C where F = (Va + 6y, 3x + 6y) C is the boundary of the region…

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Q: Evaluate the triple integral |//. z dV, where E is bounded by the cylinder y? + z2 = 4 and the…

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Q: Compute the integral SSI (2x + y) dV, where R is the tetrahedral region bounded by the planes x= 0,…

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Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: Evaluate || 4.nds , where A=zi+xj – 3y°zk and S is the surface of the cylinder x² + y =4 included in…

A: Let ∅=x2+y2-4  Then the normal to the surface S is ∇∅=2xi+2yj The unit normal is…

Q: 36. Ifo = 45x y, evaluate ||] q o dV where V is the closed region bounded by the plane 4x +2y +z =…

A: The solution is given as