6. Set up the integral /| f(x, y, 2) dV E where E is the solid that lies under x + 4y + 6z = 12 in the first octant. %3D

Q: 4) Evaluate the following integrals: a) SII (z² + + 1)ev² dx dz dy . R = [0.y] × [0.20] × [0. In 0]

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

Q: Evaluate the iterated integral. 4 1 v1-z seº dx dz dy 0 0 0

A: given  :

Q: Evaluate the triple integral |// xy dV where E is the solid tetrahedon with vertices (0,0,0), (7, 0,…

A: Consider the following: Equation of plane passing through 7,0,0,0,5,0,0,0,10x7+y5+z10=1x ​ranges…

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

A:

Q: Evaluate the iterated integral. 17 [₁₁/₁² (x² + y²) dx dy = i 17 LL" (2² + y²) dx dy

A:

Q: a) Evaluate the given integral In y TT In z dz dx dy 1 1 1

A: Finding the given integral

Q: 13. Evaluate the triple integral: In y (z) dzdydx y2

A: Given :∫12∫1x∫y2lnyz dz dy dx=I

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

A:

Q: Evaluate the iterated integral. LP'&x+yaxay (x + y²) dx dy

A:

Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: E ralu ate the given ヤyle integral: S. x² rin dy dz dx

A: Given that, The integration is, ∫0π∫0x∫0xzx2siny dy dz dx We have to find the value of this…

Q: . 3. Compute E y 2 z 2 dV , where E is the region bounded by x  1
y 2
z 2 and x 

A: The given curves are

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: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: Calculate $o (3x + 5y - cos(y)) dx + x sin(y) dy if C encloses a region of area 4.

A: To evaluate the given integral.

Q: 1. Give iterated integrals for r (x² + yz)dV where E is in the first octant bounded by the planes: y…

A:

Q: x = In(8y + 1), osys1 (a) Integrate with respect to x. dx (b) Integrate with respect to y. Ap

A: We have to find

Q: I.Evaluate the ff. iterated integrals. • 7d/2 ptan y sec y 1. .3 cos' ydxdy JJ

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

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: 16. Let D-((, y, z):05zs2, 0≤ y ≤1, 05:5z+y). Find the triple integral: 72xy³ dv.

A:

Q: Integrate fcx)9,2) =X+y -Z over thep Poth from OLo.0.0) to A (2,1,2) given by, ostsi (C) = r z i…

A:

Q: Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy

A:

Q: Evaluate the triple integral xy dV where E is the solid tetrahedon with vertices (0, 0,0), (6, 0,…

A:

Q: EVALUATE THE ITERATED INTEGRAL. ppy dxdy Jzy x – y 1. SS[ vzdxdydz 2.

A:

Q: Evaluate the triple integral // x dV, where T is the solid tetrahedron with vertices T (0,0, 0),…

A: Here we have to evaluate the triple integral , where T is the solid tetrahedron with vertices…

Q: 1)Calculate the following double integrals. (y + xy-2)dA, where R = {(x, y) E R²/ 0 < x < 2, 1 < y <…

A: Solution:

Q: 1) Evaluate the triple integral. | 6xy dV where E lies under the plane z = 1+x + y and above the…

A:

Q: 4) Evaluate the following integrals: a) (z² + 1)ey2 dx dz dy , R = [0, y] x [0,24] x [0, ln 12] b) ſ…

A:

Q: 1. Evaluate fL, 2 dv where E lies below the plane z = 2+ 3x + 4y and above the region in the…

A:

Q: 3 The integral ³³ g(x, y) dxdy is equivalent 3 to ₁ ³x g(x, y) dydx

A:

Q: 4. Evaluate fl, cos (2) dA where D is the region bounded by D = {(x, y)/ vLT <x < V3Ln,0 <y< x² }.

A:

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

A:

Q: a) Evaluate the given integral In y In z dz dx dy 1

A:

Q: #2. Evaluate the triple integral x dV, E where E is given by E = {(x, y,z) : z< x < 2z, 0 < y<x+z,…

A: Solve it

Q: 3. Show that, in the region D: 1< x<e, 0<y<In(x), the following double integral 3e4 + 1 x3 dA 16

A:

Q: 4. Evaluate x² dV G where G is a solid that lies in the first octant bounded by x2 + y? = 3z and z =…

A: We have solid G in the first quadrant bounded by x2+y2=3z and z=3 equating the above two equations…

Q: Calculate the iterated integral. '3 1. 7xy x2 + y2 dy dx + y2.

A: Given integration, I=∫03∫017xyx2+y2dy dx Use formulas, ∫xndx=xn+1n+1∫cfxdx=c∫fxdx   c is…

Q: Evaluate the iterated integral. '8. 1. 4zel dy dx dz

A:

Q: 2. Show that, in the region D: 0 < x<1, 0 <y< x², the following double integral 1 dA =- In(2) x5 + 1…

A:

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: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

A:

Q: Evaluate the iterated integral. In 3 In 4 e 4x +y dy dx 0. 1.

A:

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

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: Compute the given double integrals a) L,dy ſ (x5 – y) dx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Evaluate the iterated integral. 3 4 5 | /| (x² + y² + z²) dx dy dz -3 0 0 3 5 (x² + y? +z? ?)dx dy…

A: Application of integration

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

A:

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

A:

Q: 3. Evaluate the triple integral SSS x²y°z=dV,where E is the rectangular box given by E=

A: