10/ Compute e Fids, where S is the surface z =N16-x²-y² oriented up ward and F =

Q: . Find the center of mass of a thin plate covering the region bounded below by the parabola y = x…

A: The given curve is, y=x2 and the line y=x with density δx=12x. Sketch the bounded region as below:

Q: Compute volume under the surface x+ 2y2 above the region described by 0sxs1 and 0sysx?, shown below.…

A: Given that surface is x+2y2 and region is described by 0≤x≤1 and 0≤y≤x2. It is required to find the…

Q: Find the area of the surface generated by revolving the semicircle y = √1 − x about the x-axis over…

A: Given that, y=1-x. dydx=121-x-12·-1=-121-x 1+dydx2=1+-121-x2=1+141-x=1+14-4x=4-4x+14-4x=5-4x4-4x

Q: Find the area of the region enclosed by the curves y = x and y = 4x by integrating with respect to…

A: The given curves are: y=x2  and   y=4x The region enclosed by these two curves is given as:

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 80,0 < 0 <…

A:

Q: Calculate the derivativVe using impi dw 'w + w +wz + 5yz 0

A:

Q: Let T be the first-octant solid region bounded by the graphs of the equations y = 5(x2 + z?), y = 5,…

A: Given that T is the first-octant solid region bounded by the below equations: y=5x2+z2y=5y=45z=0x=0…

Q: Find the volumMe generated by revolving the area bounded by the giveN Curve and avd lines y = x', x…

A:

Q: Evaluate (2r+y) dV _ where V is closed region bounded by the z= 4>x and the planes x = 0, y = 0 and…

A:

Q: compute the surface area of revolution about the x-axis over the interval. y= x3, [0, 2]

A:

Q: Find the moment about the r-axis of the lamina bounded by the upper half of (x – 1)2 + y² = 1 and…

A: Given lamina:  x-12 + y2=1 The positive part of the given lamina,  y=fx = 1-x-12…

Q: 4. Finl the volume bounded by the surfaces z x2 and z 4-x2-y2.

A:

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: What is the value of the double integral Y – x sin |dA, y+ x where R is the trapezoidal region with…

A: Here we have to find the value of the given double integral ∬R sin{(y-x)/(y+x)} dA, where R is the…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30, 0 < 0…

A: According to the given information, it is required to find the area enclosed by the given curve.

Q: SI xyz dW, B is region bounded by two cylinders, wwwm w В x^2 + y^2 = 16, x^2 + z^2 = 16, and the…

A: Consider the given volume of the two intersecting cylinders given by  x2+y2=16 andx2+z2=16  as shown…

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

A:

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 95 and the upper cone z2 = 4x2…

A: We have to find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 95 and the upper…

Q: Calculate the surface area x2+y2+z2=25, between the z=1 and z=4 planes

A:

Q: 5 Compute the Surface area f obtained by revoluing the line y=x around the y-aris. a cone whichü

A: To find the surface area of cone which is obtained by revolving y=x revolved around y-axis.

Q: the voulme of the region are  bounded by the paraboloid x= y^2+z^2 and the half cone x=…

A: The volume of the region bounded by the paraboloid x= y2+z2 and the half cone x= 8y2+z2

Q: 5. Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 – x} about the x-axis.

A: Surface area

Q: Solve for the area of the portion of the cylinder x = /1 – y², which lies between the planes z = 0…

A: Here is the solution of the given problem:  By using line integral to find the surface area of…

Q: 3. Find the length of the curve y = x – In x, 1<x < 4. 1. Find the area of the surface obtained by…

A: The solution is given as follows

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the %3D Vr2 + y? with…

A:

Q: 2. Find the surface area when y = 2\x with 1 < x < 3 is rotated around the x axis.

A:

Q: find the center of mass of a thin plate of constant density d covering the given region. The region…

A:

Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

A: Solution is given below:

Q: Find the area of the surface given by z=f(x,y)=3+x3/2 over the region R, which is the rectangle with…

A:

Q: Subject:MMP

A:

Q: Find the area of the surface given by z = f(x, y)  that lies above the region R. f(x, y) = 13 + 9x…

A:

Q: 3. Find the surface area generated by rotating y=- bounded by y=0_ x=0 , and x=9 about the the…

A: Surface area generated by rotating a curve y = f(x) about the x-axis from x = a to x = b is given by…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 77 and the upper cone z2 = 3x2…

A: We have to find the volume of the 'ice -cream' that is bounded by the sphere  x2+y2+z2 = 77 and the…

Q: Find the area of the surface generated by revolving x = 6t and y = 4ť (0 < t < 1) X

A: answer is in next step

Q: Find the surface area generated by y = x³; x = 0 and x = 3 and is revolved on x-axis.

A:

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 10, 0 < 0…

A:

Q: Given the curve y=2x^0.5 and line x =y. Find the area bounded and the  distance from the x axis to…

A: Given the curve y=2x^0.5 and line x =y. To find: Find the area bounded and the  distance from the x…

Q: Find the volume generated by the region bounded by the curve y 12X and the line X3 rotated about the…

A:

Q: How far is the centroid of the area boundded by the curves y=e^x, y=e^-x, and x=1 measured from the…

A: We have to find the distance of centre of mass from y Axis  So , find only x coordinate of centre of…

Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

A:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 5x + 5y R:…

A: The surface bounded by z=f(x,y) that lies above the region R.f(x,y)=5x+5yR: triangle with vertices…

Q: ryz dV if S is the region bounded above by 2? + y? + 2² = 16 and below the %3D 1² + y² with dV…

A: To evaluate the given integral, convert the Cartesian coordinates into spherical coordinates. Use…

Q: Sketch the region enclosed by the given curves. y = 4/x, y = 16x, y =x, x>0 16 y y 10| 10- 8 6. 2 4…

A:

Q: Find the area of the surface given by f(x, y) = 8 + 4x – 5y that lies above the region R= {(x, y) :…

A: The surface f(x,y)=8+4x-5y that lies above the region R=x,y:x2+y2≤1.

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4x + 4y R:…

A:

Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y-y3, x…

A: Consider the graph:

Q: Calculate the area of the surface defined by r = 5, 0<0<Tl4,0<¢<n/2.

A: Please see the explanation below

Q: compute the surface area of revolution about the x-axis over the interval. y = x, [0, 4]

A:

Q: Find the volume of the 'ice-cream' that is bounded by x² + y2 + z2 = 10 and the upper cone z2 = 4x2…

A: