4 The area of the surface S = {(x, y, z) E R³ : z = 5 – z2 – y², z > 3} equals (A) 47 (B) 13 (C) (D) 3"

Q: Find the area of the surface x2 - 2 ln x + sqrt(15)y - z = 0 above the square R: 1<=x <= 2,…

A:

Q: (B) Integrate g(x,y,z)=x+y(x+2z) over the surface area of the region cut from plane x+2y+2z=5 by the…

A: What is Surface Integral: Surface integral is an iterated integration that is performed over a…

Q: Where is the centroid of the region bounded by y = 4-x2 and the x-axis?

A:

Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y-2)² = 2x -2, S4: x = 0, S5: y =…

A: To find- The Solid bounded by the surfaces S1 : 2x + 3z = 6, S2 : y = 2, S3 : y - 22 = 2x - 2, S4 :…

Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

A:

Q: The region bounded by x = 1 - y¹, x = 0 is rotate about the line y = -5. The volume of the resulting…

A:

Q: d the volume V of the solid obtained by rotating the region bounded by the ren curves about the…

A:

Q: Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant

A:

Q: 11. The solid whose base is the region bounded by the semicircle y = V1 - x² and the x-axis, and…

A:

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: What is the solid of revolution obtained when you revolve the region bounded by the curves y=x−1,…

A: We have given curves y=x-1,  y=0 and x=3 And we can plot graph of these curves as We can  see here…

Q: Find the potential u(x, y) for u +u =0 in the rectangle 0<x< 2 and 0 < y s 2, if the upper side is…

A: The given problem is to solve the potential u(x,y) Laplace partial differential equation, we have to…

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

A: We have to find volume.

Q: The surface area of the solid generated by revolving the straight line 2y = x+1 bounded by x-1, x 3…

A:

Q: 22 Find the Volume of the Solid of revolution bound al by the circuit x*+y=16, aud the lineSX=0 and…

A: Equation of the circle is given as x2 +y2 = 16 x2 +y2 = 42 Where radius of the circle r is 4 unit…

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: 9. Evaluate 18x dV where E' is the region behind the surface y = 4 - 2² that is in front of the…

A:

Q: A lamina is in the shape of the region bounded by the lines x = 1 and y = 2, and the parabola y =…

A: Let's find.

Q: 11. xyz dV, where G is the solid in the first octant that is bounded by the parabolic cylinder z = 2…

A: To evaluate the triple integral

Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

A:

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: 4. Find the volume of the solid under the surface f(x, y) = xy and above the triangular region in…

A: .

Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: 4. Find the volume of the solid generated when the region bounded X - 2 by f(x) = x = 1, and the…

A:

Q: Find the center of mass of a thin plate covering the region between the x-axis and the curve y =…

A:

Q: valuate the double integral. (x2 + 2y) dA, D is bounded by y = x, y = x³, x 2 0

A:

Q: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

Q: 2. Evaluate the triple integral where E is the solid bounded by y = 2x² + 2z² and the plane y = 8.

A: A detailed solution is given below.

Q: 2. Set up the integrals for the work required to pump the water in the drum shaped solid to the goal…

A: Work done= Force * distance                     =(force due to Weight)* distance

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: compute the surface area of revolution about the x-axis over the interval

A: The given function is

Q: Example 16. Find the volume of the region D enclosed by the surfaces z = x² + 3y² and z = 8 – x2 -…

A:

Q: ds k(4nr). dt --Select-- %3D volume dV k dt surface are ds - ). dt dV dt dV = k(4tr²). dt

A: Given evaporation rate proportional to surface area Use formula of volume and surface area to find

Q: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

A:

Q: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

A:

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

A:

Q: 2. The solid bounded by y = 0, x = y², x = 4, and z = Octant (ie. x, Y, z > 0). 2x in the First

A:

Q: | 5z2 dV , where E is Evaluate E the region bounded below by the cone z = Vx2 + y² and above by the…

A: Given: ∫∫∫E5z2dvz=x2+y2x2+y2+z2=1

Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

A:

Q: 1 Find the centroid of the area bounded by x2- 4y + 8 = 0, the lines x = 0 and x = 4, and the…

A: Formulas are written within the solution.

Q: 7) Find the area of the surface that is formed by revolving the function y = 2 x on the interval %3D…

A:

Q: 2. Find the area of the surface obtained by revolving the curve g(x) = Vx +1 on the interval 0 < x <…

A:

Q: 3.) Find the area of the surface given by f (x, y) = 9 – x2 over the region R: square with vertices…

A: Given: fx,y=9-x2

Q: Compute the surface area of revolution of f (x) (x + 1)z about the x-axis over 3 [0,1]

A:

Q: Find the solid of revolution that results when the region under the graph of f(x) = xvsin x for 0< x…

A:

Q: 2. Find the surface area of the solid generated by rotating the region bounded by the graphs of f(x)…

A: In this question we have to find the surface are of the solid region generated by rotating the…

Q: 2. Set up the integrals for the work required to pump the water in the drum shaped solid to the goal…

A: set up the integral for w9rk requireded to pump the water in the drum shaped solid to the goal line

Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…

A:

Q: Determine the surface area of the part of z = 13 - 4x2 - 4y2 that is above z = 1 with x <1 and y <0.…

A: Surface area:- The total area of all the faces of a three-dimensional object is its surface area. We…

Q: The solid bounded by the surfaces S : -2(: – 2) = y² S2 : 1 = 5– 2y S3: r=0 S4 : y = 0 Ss : z = 0…

A: