4. if (r+r³)d m is the x coordinate of the center of mass of a rectangular sheet R with m being the mass of the rectangular sheet, m/= 0. We can confirm with complete certainty that the moment of order 1 Mx of the sheet with respect to the y-axis is given by

Q: 2set up but do not evaluate an iodegoral thatreprsedtsthe lvolume of the solid of rerolution…

A:

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

A:

Q: 3. For all a? + y + 2? > 0, verify that the velocity potential 1 $(r, y, z) = Vr? + y² + z2 is a…

A:

Q: In the absence of a damping mechanism, the deplacement, go, helners cons tant k suspended oloject°…

A:

Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent is constant and the…

A: The given curve is y=bexa.

Q: 4. Evaluate the integral f. x'y°dy – x°y'dx, where C is the square determined by the lines x = 0, y…

A: As per Bartleby's answering policy, we can answer only one question and here we have answered the…

Q: Fi for oec ind volume of the solid of revolution by rolahng about the -ais each regton boundad b the…

A: To calculate the volume of the given solid of revolution

Q: The volume of the solid generated by the curve y = e, between z = 2 and z = 6 about the z- azis is

A: Given: The curve is y=e-x   To determine: The volume of the solid generated by the curve y=e-x…

Q: 6 foND THE EXACT LENGTH Of THE zt -2t PARAMETRIL y(e)=1+4t CURVE X= e te

A:

Q: 1. If F= (y,z,x), the outward flux through a smooth closed surface (a) depends on the surface. (b)…

A: Given, F=y,z,x We know,  Flux by the Gauss divergence theorem. ∬F.ds=∬∫divF.dvF=yi+zj+xk If you…

Q: Consider the solidas bound below by 3: N3C82+y?), above by ?-1= N @ Its volume V (s); O The height…

A: Here we will use cylindrical co ordinate  x= r cosθ , y = r sinθ , z=z    and    dV= r dz dr dθwhere…

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

A:

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &3, x2-y2=3 &4 Where u=xy and v=x2-y2

Q: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xi +…

A:

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

A:

Q: Evaluate the integral | (3x – 2 y + :)ds where C is the curve, C, and C, as shown. 3- y² + z² 2. 3…

A: Here, Curve C is equivalent to c1+c2. The point of intersections of c1 and c2 is at 0,1,0.

Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x…

A:

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

A:

Q: (10) Find the work done by F = -yi+ xj+ zk on a particle moving along the helix r(t) = where 0 < t <…

A:

Q: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xỉ +…

A: Given: F(x, y, z) = 2xi + y + zk along, almost every where with z = x² + y² paraboid and z = 2x…

Q: 1. Use the cylindrical coordinate to evaluate ff. x² + y²dV _where G is the solid bounded by…

A:

Q: Find of the ay+2²7 the revolving Curve x = 2 0≤y in 2 about the y-axis is The area, S, of the…

A:

Q: (7) Determine the upward flux of ▼ × F through the part of the elliptical cone C = {(x, y, z)|z = 2…

A:

Q: The solid S is obtained by rotating the region enclosed by y = f(x) 2 0, a = 5+ 5e6 1- e6 5+ 5e16 1-…

A: The given question is solved below.

Q: 8) Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y?…

A:

Q: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

A:

Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

A:

Q: 1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr…

A:

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: Set up an integral to compute the arc length L of the curve C: r(t) = (, 4t, v2t) %3D from the point…

A: I am going to setup an integral to compute the arc length of the given curve using the required…

Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

A:

Q: Evaluate /|/ (x² + y² + z²)² dV where E is the solid ball centered at the origin with radius 2.

A:

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: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y,z) = 2xi + yj…

A:

Q: 27) If the solid of revolution formed by rotating R2 about the y-axis is a cylindrical shell, then…

A: You have posted multiple questions. As per the instruction, we will be answering only the first one…

Q: Given the curve y = x' and the line y = 2 – x. Find the moment of R with respect to the y-axis М of…

A: Given problem:- Given the curve y = x2 and the line y = 2-x. Find the moment of R with respect to…

Q: Use numerical integration with Ax = 1.0 m to locate the centroid of the surface generated by…

A: Given That : y=3x216 and ∆x=1.0 m To find : locate the centroid of the surface generated by…

Q: 1. Compute the average height of the cone z = a> 0. r² + y² above the disk x² + y² ≤ a² for

A:

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

A:

Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm³, thermal…

A: The equation is u t…

Q: The measurements x1 = 10m, x2 = 8m, and x3 = 6m represent the sides of a rectangular parallelepiped…

A:

Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: 4) If a wire in the shape of the helix: x = 2 sin t,y = 2cos t,z = 3t;0 <t < 27, and the density is…

A:

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: 1. Find parametrizations of the curve of intersection of x² + 4x + z² = 0 and x- – 2y + z = 3.

A: Given curve is x2 + 4x + z2 = 0 .  This can be written as (x+2)2 + z2  = 4  So the curve is a circle…

Q: Compute the surface area of the cone generated by revolving c(t) = (2t + 2, 6t) about the x-axis for…

A:

Q: A 3 cm length silver bar with a constant cross section area 1 cm" (density 10 g/cm, thermal…

A:

Q: Compute the integral 10x/1+ 4y?ds over the curve C: R(t) = (t + 5, t), 0<t< 1.

A:

Q: Show that at any point (x,y) on the curve y = be", the length of the subtangent is constant and the…

A: