1 Evaluate dV, where E lines between the spheres a? + y? + z² = 25 and %3D x² + y? + z2 49 in the first octant. a? + y? + z?

Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: 1 Evaluate E 22 + y² + z² dV, where E lies between the spheres a? + y? + z² = 16 ar ² + y² + z² = 25…

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Q: Evaluate I = , dx dy where R is the region that lies inside the circle x2 + (y – 2)2= 4 and outside…

A: We have to find ∬Rdxdy where R is the region that lies inside the circle x2+y-22=4 and outside the…

Q: 7. Evaluate * SS $6(x² + y² + z?)dV B where B is the ball with center at the origin and radius 1 8л…

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Q: e (2 +y+2) dV, JIIE V + y? + z? where E is the region bounded by the spheres a? + y? + 22 = 1 and r2…

A: ∭e-x2+y2+z2x2+y2+z2dv

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Q: 4. Which would not be sufficient to prove AWXZ AWYX? C ZWXZ = LY WZ А WX XW YW WZ D WX WX XY XZ WX…

A: To show that the given two triangles are similar we need to show that the sides of the two triangles…

Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z? = 16 and x2 + y2 + z2 = 64 in the first…

A: The region E lies between the spheres: x2+y2+z2=16  and  x2+y2+z2=64  in first octant.

Q: 1. Evaluate SSSE z dV where E lies between the spheres x2 + y? + 2² = 1 and a? + y² + z² = 4 in the…

A: Given, ∫∫∫EzdV where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4 in the first octant.

Q: Evaluate (l. yz dV where E lies above the plane z = 0 and below the plane z = y, and inside the…

A: Given, ∫∫∫EyzdV, Where E lies above the plane z=0 and below the plane z=y and inside the cylinder…

Q: Given z = 15 In(t) and y = 225 t then find %3D dy dx d'y dr2

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Q: Compute the irertia móment by x ( Ix=Sy?JA) tor number off segment n=s hyte multple-trapezoidal…

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Q: Evaluate ſ[ſp z dV where E lies between the spheres x² + y² + z² = 1 and + y*¨+ 2² = 4 in the first…

A: Solution:

Q: 1 Evaluate dV, where E lies between the spheres x + y + z = 16 and + y? + z2 = 64 in the first…

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Q: Find thequahen. perpenditar to i fine -個 epe at OD pr Find tha liit ultpy cen gale (ro a) Po FO…

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Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: The line integral 2xe" dæ + a²e" dy + (1 – 2²)e¬²² dz is not independent of path.

A: The line integral ∫CF·dr is independent of path if the curl of F is zero, that is, ∇×F=0. Here, The…

Q: find the indicated extrema, assuming that x, y, and z ar = xyz z - 12 = 0

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Q: Evaluate dV, where E is the solid in the first octant bounded by r2 +y? + z2 = 1 E and a2 + y? + z2…

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

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Q: (0s 2. Evaluate SLla xex?+y²+z4) dx dy dz, where R is the upper half of the unit ball, x2 y2 + z2 <1…

A: The given integral is,

Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

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Q: Evaluate ||| Vx2 + y2 dV, where E is the region that lies inside the cylinder x2 + y? = 25 and…

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Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: Eхample : Evaluate the triangle fxy dy - y? dx around the square cat from the first quadrant by the…

A: Given problem is :

Q: 10- Evaluate JJI where E is the region that lies inside the cylinder Vx2 + y?dV E x? + y? = = 16 and…

A: Here we use polar coordinate and Jacobian .

Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: 1 Evaluate dV, where E lies between the spheres x2 + y2 + z2 = 9 and x2 + y? + z2 x2 + y? + z2 36 in…

A: we want to find the triple integral ∫∫∫E1x2+y2+z2  dVwhere E lies between the sphere x2+y2+z2=9  and…

Q: dz Given z = e* sin y,x u? + v2,y = uv, find - dv %3D %3D

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

Q: 1. Evaluate ſf, y dS where S is the portion of the cylinder 4x² + 2y² = 16 that lies between z = 0…

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

Q: 1 I. Evaluate dV, where E lies between the spheres x? + y² + z² = 1 and x2 + y? + z² E x2 + y? + z?…

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Q: 22. Evaluate xyz dV, where E lies between the spheres p - 2 and p- 4 and above the cone - 7/3.

A: Solution:-

Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: O Given the initicl bouridary conditions y(0) =0, y'c0) = 1, letrmine the, solntiem of %3D…

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Q: 16. Evaluate * :- S S $6(x² + y² + z? )dV В where B is the ball with center at the origin and radius…

A: (16).  We have to find the integral∫∫∫B 6x2+y2+z2 dV  ;      where B is the ball with center at…

Q: . The uejveciion of a beam is governed by the equation d'y + 81y = 0 (x) dx %3D where o(x) is given…

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Q: 25. Consider the equationdy/ dx = (y − 4 x)/( x − y) .a.Show that equationcan be rewritten as (30)…

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Q: Evaluate /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…

A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.

Q: 5. Evaluate SS (x² + y²) dV,where E lies between the spheres x2 +y² + z² = 4 and x² + y² + z² = 9

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Q: 1. Evaluate ſſ, y dS where S is the portion of the cylinder 4x² + 2y² = 16 %3D that lies between z =…

A: Given S is portion of cylinder 4x2+2y2=16 that lies between z=0 and z=7. Parametrize the surface s.…

Q: (yz) : (a+y+Z) %3D tos he Since , Luv) = udv + vdu dx dn

A: It is partial derivative problem

Q: 16. WXYZ is an isosceles trapezold with WX ZY If mĐW = (2x)° and mĐZ = (x +27)°, find the value of…

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Q: Find dy/du, du/dx, and dy/dx when y and u are defined as follows. and u = Vx + 3 V = - dy du du dx 3…

A: Trigonometric identities: 1.d/dx(xn)=nxn-1 2.d/dx(constant)=0 3.d/dx(root x)=1/2root x And given y…

Q: +/ Let S= (D) where D ={(v,w): u? tz? < 1,vy0 v 710} and ē Cv,zz)= (2u+1, U-v,3ut v) Calculate the…

A: Given that S=ϕ(D), D=u,v:u2+v2≤1,u≥0,v≥0ϕu,v=2u+1,u-v,3u+v The domain of the surface is 0≤u≤1, 0≤v≤1…

Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z² = 16 and E x2 + y? + z2 x? + y? + z?=…

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Q: 1 SI. Evaluate dV, where E lies between the spheres x2 + y? + z? a2 + y? + z2 = 1 and æ? + y? + z²…

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: Find dyldy and xz4 Sint, y² Scost, OCtca24 For which vakes Of t is Hhe cure concave puars? anguer n…

A: x=4sint  , y=5cost

Q: Use Green's Theorem to evaluate |. (y? – 6y) dx + (y³ + 10y²) dy where C is shown below.

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