3. Evaluate if G is a solid in the first octant bounded by the plane y+ z = 2 and the surface y = 1– r².
Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…
A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…
Q: Find [[fw ryz dV if W is the solid region in R³ below the surface z = x² + y² and above the square 0…
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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: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…
A: Parametrize the three curves separately and c is the sum of the three integrals.
Q: If F= 2y I- 3J +x²k and s the surface parabolic cylinder y= 8x in bounded by the planes OF the 2.…
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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: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D
A: In this question, we have to write the triple integral to find the volume of the solid bounded by…
Q: 4. Find the volume V of the solid S that is bounded by the elliptic paraboloid defined by 2x2 + y2…
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Q: Let R denote the solid in the first octant bounded by the planes 2x + 6y + 3z = 6, x = 0, y = 0, z =…
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Q: Find the Volume 6t prime bounded Parabolid ( top Surface) z = x'+y regi on in M=2y, ソ=o the by the…
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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 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: Integrate G(x, y, z) = y + z over the surface of the wedge in the first octant bounded by the…
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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: a) Let G be the wedge in the first octant that is cut from the cylindrical solid y² + z² ≤ 4 by the…
A: To Evaluate: ∫∫∫GxyzdV. Where G: y2+z2≤4, y=2x , x=0. As per policy, we are solving only thr first…
Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…
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Q: Use Stoke's theorem to evaluate the integral xydx +x*dy– 4x'ydz where C C is the boundary of the…
A: Given: ∫Cxydx+x2dy-4x3ydzBoundry square surfaces z=1vertices are (1,0,1),(1,1,1) & (0,1,1) &…
Q: Evaluate where G is the solid in the first octant bounded by paraboloid : = + y, the cylinder r+ y 9…
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Q: Evaluate fF.ndS, where F-4xi-2y' j+z'k and S is the surface bounding the region x' +y' =4, and the…
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Q: 8. Use Green's Theorem to calculate f, x?y³dx + (xy - y?)dy where C is the boundary of the region…
A: The given integral is ∫Cx2y3dx+xy-y2dy, where C is the boundary of the region lying between the…
Q: 9. If F = (x – z) î + (x³ + yz)ĵ + 3xy² k and S is the surface of the cone z = a – Va? +y?) above…
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Q: Evaluate. where G is a solid that lies in the first octant bounded by x^2 + y^2 = 3z and z = 3.
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Q: Consider the solid whose base is the region bounded by 4x? + 9y? = 36. Y 3 -3 -2 -1 -1 2 3 2 -3 1.
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Q: If E is the solid shape bounded by x 20,y 20,z 20 and the plane 6x + 4y + 3z = 12 evaluate %3D (y +…
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Q: Evaluate .n dS and .ndS if F = (x + 2y)i– 3zj +xk, , and S is the surface of 2x + y + 2z = 6 bounded…
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Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…
A: triple integral
Q: 1) Consider the solid Q in the first octant, generat surfaces: z = (y – 3)² + 1, 2r + 4z = 16, 1= 1,…
A: Volume of solid: Let z=f(x, y) and z=g(x, y) be the functions of x and y of a solid, and let x=a to…
Q: 10/ Compute e Fids, where S is the surface z =N16-x²-y² oriented up ward and F = <y,-x, zZ %3D 工=?
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Q: 3. Evaluate AP G if G is a solid in the first octant bounded by the plane y + z = 2 and the surface…
A: The given problem is to evalute the triple integral over the given surface of first octant bounded…
Q: 1. Find the surface area of the cone z = Jx2 + y2 that lies between the plane y = x and the cylinder…
A: Surface area in xy-plane
Q: Evaluate G if G is a solid in the first octant bounded by the plane y +z = 2 and the surface y = 1–…
A: Use the following formulae, to obtain the solution. a-b2=a2-2ab+b2∫xndx=xn+1n+1+C
Q: Use divergence theorem to evaluate where F(x, y, z) = 3xi + xyj + 2xzk and s is the surface of the…
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Q: In each of the following cases, draw each solid Q bounded by the surfaces whose equations are given…
A: To graph the below surface that is in the first octant. x2=−z−3z=2y+z=3
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: A solid G is bounded by the paraboloid z = 4 – x2 – y?, the cylinder x2 + y? = 4 and the plane z =…
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Q: Evaluate x dV , where E is the E region in the first octant bounded by the sphere x² + y² + z² = 1…
A: given region is in the first octant. using spherical coordinates x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ and…
Q: Find the points on the surface xy + yz + zx - x- z =0 where the ant pla
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Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…
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Q: please help me as soon as possbile
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Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0
A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.
Q: Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = the planes x = 0, x =…
A: Here I am using simple tripple integration to solve this question.
Q: Use Stoke's theorem to evaluate the integral xydx+x'dy – 4x’ydz where C is the boundary of the…
A: Here the surface is the plane of the square with vertices A1,0,1, B1,1,1, C0,1,1 and D0,0,1. To…
Q: Let S be the piece of the surface z = 9-r that lies inside the cylinder r2 +y² = 9, and let F = (x,…
A: Given, S be the piece of the surface z=9-x2 that lies inside the cylinder x2+y2=9, and let F=x,y2,z.…
Q: Let the surface Σ be the solid bounded by the paraboloid z “ 1 ´ x2 ´ y2 and the xy´plane.…
A: Use Gauss divergence theorem to compute the outward flux.
Q: a) Evaluate the surface integral ſ 2x²y dS over the surface y² + z² = 1 betwee x = -1 and x = 5.
A: a We have to evaluate the surface integral ∬σ2x2ydSover the surface y2+z2=1 between x=-1 and x=5.…
Q: where E is the region bounded by the paraboloid y= r+ z2 (Figure 15.4. %3D y = x2 + z?
A: Please rate and feel free to ask any query about any part of the question .
Q: Use Stokes' theorem to calculate (V × A) · ndS with A = 3yi – xzj+ yz²k, where S is the surface of…
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Q: 1. Evaluate the surface integral SL xz² ds ; o is the part of the cone z = Vx2 + y² that lies…
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Q: Use Stokes’ Theorem to evaluate F(x, y, z) = 3zi + 4x j + 2yk; C is the boundary of the paraboloid…
A: Use Stokes theorem
Q: 3. Use Greens theorem to evaluate (e* + y²)dx + (e' + x²) dy where c is the boundary of the region…
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Step by step
Solved in 2 steps with 2 images
- Find the area of the surface x^2-2y-2z =0 that lies above the triangle bounded by the lines x=2,y=0 and y=3x in the x-yplaneEvaluate. where G is a solid that lies in the first octant bounded by x^2 + y^2 = 3z and z = 3.Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z = -x^2/4 - y^2 O z = y^2 - x^2/9
- Find the image of the Gauss map of the FINITE portion of the paraboloid z = x^(2) + y^(2) , z smaller than or equal to 1 with respect to the outward unit normalEvaluate ∫∫∫E 1/(x^2+y^2+z^2 )dV where E lines between the spheres x^2+y^2+z^2=4 and x^2+y^2+z^2=16 in the first octant.Find the volume of the solid that lies under the elliptic paraboloid /4 + y219+2-1 and above the rectangle R-[-1.13* [-2, 21. X
- A region R consists of a square bounded by the lines x = −7, x = 7, y = 0, and y = −14and a half disk bounded by the semicircle y = (49-x^2)^(1/2) and the line y = 0.Find the center of gravity, (x, y), of R.Find the surface area of the part of the surface z=x^2+3ythat lies above the triangular region T in the xy-plane with the vertices (0, 0), (1, 0), and (1, 12).Give your answer in 2 decimal places.You have to use the following formula:An integral expression for the area of the surface generated by rotating the curve X =Vv, 1sys8 about the x-axis is S 2 TX°Vdx 1+ 3x* 2 TTX .2 2 TIXV1+ 3x2 dx S, 2 nx*V1+ 9x*dx 3 2 TXV1+9x2 dx