5. Evaluate y* dV, where E is the solid tetrahedron with vertices at (0,0,0), (2,0,0), (0, 2,0), and (0,0, 2);

Q: 1. The solid that is above by the paraboloids z = 2- x² – y² and below by the paraboloids z = x? +…

A:

Q: 46.) (a) Parameterize S the 1st octant portion of the cylinder y² + z² = 9, 0 <x<4 (b) Use above to…

A: y2+z2  0≤x≤4x=uy=3 cos vz=3 sin vparameterise the surface ass(u,v)=(u   3 cos v   3 sin v)0≤u≤4,…

Q: Evaluate 3zdV E where E is the solid enclosed by z = 1 and z = x + y

A: we need to evaluate the given integral about the solid E . first we will find the limit of the…

Q: 14. Evaluate o 4y dr + 3r dy, where C is the trapezoid with vertices (0,0), (2,0), (6, 2) and (0,…

A: The solution are next step

Q: Calculate the double integral Sle (x² + 2y) dA, where R is the triangular region with vertices 8/3…

A:

Q: Verify Green's Theorem by evaluating both integrals y2 dx + x² dy = dA ду for the given path. C:…

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

Q: Evaluate the triple integral ∫∫∫T (x^2) dV where T is the tetrahedron with vertices (0, 0, 0), (1,…

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Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

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

Q: 14 13 12 11 10 9 8 7 4- 3- 2- Find the volume of the solid S obtained by rotating R about the line y…

A: Here R is the region bounded by y=9x,x=2.5 and the x-axis i.e.(y=0)and the solid…

Q: 5. Evaluate Fale JJJ (²+ + ² dv, where a, b, c > 0, and & is the region given by E 22 + y² 2² 6² +2…

A: Given triple integral is ∫∫∫Ex2a2+y2b2+z2c22dVa,b,c&gt;0x2a2+y2b2+z2c2≤1 in the first octant. Now,…

Q: (34) Compute SSp (6e3y + 1) dA where D is the solid triangle with vertices (0,0), (1,0), and (1,2).

A: Equation of the linejoining the points 0,0 and1,2  is  y-0x-0=2-01-0  Or,  yx=21=2  Or, y=2x…

Q: Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices…

A: Given Data : Triple Integral ∬∫ExydV and E is the solid tetrahedron with vertices 0,0,0,…

Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

A:

Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

A: Introduction: By applying Green's theorem, one can determine line integral through surface integral.…

Q: 2. Consider the DE y(4) – 4t²y" + 4y" = 0. (a) Is the DE linear? (b) Is the DE homogeneous? Why? (c)…

A:

Q: (2) Find the integral (0,2,0) and (0,0,1). where D is the tetrahedron with vertices (0,0,0),…

A: Given : ∬∫x+2y+z dV             where D is  tetrahedron with vertices 0 ,0 ,0  , 1 , 0 , 0  , 0, 2 ,…

Q: | eョで)) dV=

A: Given:              ∭Dex2+y2+z232dv        d is the region in the first octant between spheres…

Q: 18. Evaluate § (9 − x² − y²) dV, where H is the solid hemi- sphere x² + y² + z² ≤ 9, z ≥ 0.

A:

Q: 11 10- 9 8 7 6 5- 3 Find the centroid of the region displayed in the graph. (x, y) = 4

A:

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

A:

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: (b) ſf f(x,y) dA if f(x, y) = y², where R is the triangular region with vertices (0, 1), (1, 2) and…

A:

Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

Q: 2. Set up the triple integral f[Sp I+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

A:

Q: 11. The y-coordinate of the centroid of the solid in part IV is.. A. 0 В. 1 С. 2 D. 3

A:

Q: Evaluate the triple integral II. x* dV, where T' is the solid tetrahedron h vertices (0, 0, 0),…

A:

Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

A:

Q: 1.Let 3 le the solid obtained by rotating by region shown in the fiqure about the Assume as3 and b=…

A: Given: y=ax(x-b)2 and y=0 and  0≤x≤b The rotation about the y-axis. Assume a=3 and b=1

Q: 3/5ketch, E Valuate & reverse the order of in tegration 2. ol X dy

A: We are looking at the following curves simultaneously: y = ex y = 1 x = 0 x = 2

Q: Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with…

A:

Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: . Set up the triple integral fSSp r+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

A: The equation of tetrahedron with intercepts (a,0,0), (0,b,0) and (0,0,c) is given by: Given…

Q: Evaluate the triple integral III xy dV where E is the solid tetrahedon with vertices (0, 0, 0),…

A: The given integral is, ∫∫∫E xydV Here E is the solid tetrahedron with vertices O0,0,0, A10,0,0,…

Q: 1. Draw a sketch of the cylinder z= ==V36 – 4y2.

A: Given: z=1336-4y2

Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: 2 -4 5) Evalate SSx dxdy, where D is the region bounded 2. by the hyperbolas *y=2, xy=4 and the…

A:

Q: 4. Evaluate ryz dV, S is the solid in the first octant S bounded by the cylinders x² + y² = 4 and x²…

A:

Q: In his work Nova stereometria doliorum vinariorum (New Solid Geometry of a Wine Barrel), published…

A:

Q: 1. Evaluate the integral ryz dV, where E is the tetrahedron with vertices (0.0,0), (2,0,0), (2,3,…

A: The vertices of tetrahedron are (0, 0, 0), (2, 0, 0), (2, 3, 0) , (2, 0, 4). The equation of the…

Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

Q: 1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2…

A:

Q: 4. Evaluate x²dV G where G is a solid that lies in the first octant bounded by x? + y? = 3z and z =…

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Q: ³ SS ²0 Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), an

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Q: What is the additional condition for a cubic-spline S(x) that passes through n data points (x1, Y1),…

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Q: Find ff -6xydA over the D triangular region D with vertices (0,0) (2, 0), (0, 4)

A: problem is related to double integration

Q: 2. 7 3. Find the centroid of the region bounded by y 3, 3 to the nearest thousandth. nd Since you…

A: To find the centroid of the given region R by integration

Q: Example 5: Find fff, Vx2 + z²dV, where E is the region bounded by the paraboloid y = x2 + z2 and the…

A: Cartesian co-ordinate and polar co-ordinate x=rcosθy=r sinθx2+y2=r2θ=tan-1yx

Q: 8 9 10 11 e centroid of the region displayed in the graph.

A: Topic:- Geometry

Q: 1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,…

A: Given: The function with two polygonal paths in space joining the origin to the point (1, 1, 1).…