Reduce the surface integral ( S A.ds) of a cube of sides parallel to the three perpendicular axes, one of its angles at the origin, and the length of each of its sides equal to one unit Note that: A=ix^2y

Q: Find the area of the surface generated by revolving x= 4/9 - y,0sys about the y-axis. 16 x=49-v 12

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Q: 10 Find the area of the surface generated by revolving the region bounded by. ISKSS about the…

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Q: Find the surface area of the portion of the half ball with a radius a which cuts off by the cylinder…

A: To Find: The surface area of the portion of the half ball with a radius a which cuts off by the…

Q: a) Find the volume and the lateral surface area of the solid formed by rotating this func- tion…

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Q: Compute the surface area of revolution about the ?-axis over the interval [0,?] for ? = 6sin(?).

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

A: Given, r=3θ,  0≤θ≤5.4

Q: Find the volume of the solid generated of the area in the first quadrant bounded by y = 3x – x³, x =…

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Q: 2. Find the surface area generated by revolving the circle x = cost, y = 1 + sint, 0sts2n over x -…

A: Use formula of area about x axis

Q: (1 point) The volume of the solid obtained by rotating the region enclosed by y = a², y = 2x, about…

A: y=x2y=2x about line x=2 for point of intersection x2=2xx2-2x=0x(x-2)=0x=0,2

Q: Find the surface area of revolution about the x-axis of R.

A: Given curve y=2x, 2.3≤x≤4.2 We have to find the surface area of revolution.

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³.

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Q: Find the change in the lateral surface area of a right circular cone, with radius of base fixed as…

A: The lateral Surface area of a right circular cone is given as A =πrh2+r2        A2 =π2r2(h2+r2)…

Q: 8. Find the volume of the solid whose base is the semicircle y = V9 – x², where -3 sIS 3, and whose…

A: This question is based on application of integration.

Q: A metal plug has been designed using the intersection of the two cones z = √√x² + y² and √x² + y² +…

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Q: By using double integrals, find the surface area of plane 2x + y+z = 10 that lies inside the…

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Q: Find the surface area of revolution about the x- axis of y = 3 sin(5x) over the interval Preview

A: Given curve is y=3in(5x), firstly, we will find dy/dx

Q: Evaluate the integral xyzdV where E lies between the spheres with radius 2 and 4 and above the cone…

A: Using spherical coordinates,

Q: Use triple integral to show that the volume of a sphere with radius 'a' ra". is

A: We have to use triple integral to show that volume of sphere with radius ' a ' is 43π a3. Equation…

Q: Find an integral for the area of the surface obtained by rotating y = √25-x, 9 ≤x≤ 16, about the…

A: To find an integral for the area of the surface obtained by rotating the below equation about the…

Q: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

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Q: Determine the surface area generated by revolving the arc 3y= 4x from x=0 to x=3 about the x-axis.

A: To find- Determine the surface area generated by revolving the arc 3y = 4x from x=0 to x=3 about the…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: y = } + sxs1 <x<1 2

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Q: Find the surface area generated by revolving y=7x+6 about the x axis on the interval [0,6]

A: We need to find the surface area generated by revolving y=7x+6 about the x axis on the interval…

Q: Find the surface area of revolution about the y-axis of y VOur ancwor in torme of round to docimal…

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Q: 4. Determine the surface area of the solid obtained by rotating y = v9 – x², -2 <x<2 about the x –…

A: Let's find.

Q: Use either a computer algebra system or a table of integrals to find the exact area of the surface…

A: Solution

Q: to cylindrical triple intesmal, Where Convert integral E is the finst atent bonded by z=1-x²-y²

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Q: Set up the integral for the surface area of the solid created by revolving y= Vx 1< x <8 about the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Set up triple integrals for the volume of the sphere r = 2 in(a) spherical, (b) cylindrical, and (c)…

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Q: 3. Find the volume of a sphere with radius r by integration.

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Q: Find the center of mass of solid revolution if an area in Ist Quadrant (Kuadran Pertama) bounded by…

A: Given functions are Intersection points Area of region is Centre of mass revolution

Q: Q3: Develop the lateral surface of a hexagonal prism of base edge 20mm a on its base on HP such that…

A: Given: To explain the given statement as follows, To develop the lateral surface of a hexagonal…

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: Find the surface area obtained by revolving the parabolic arc y2=x from (0, 0) to (9, 3) about the…

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Q: Find the surface area of revolution about the x-axis of  y= 4sin(4x), from x is greater than or…

A: Equation of curve is y= 4sin(4x) The interval is 0≤x≤π2

Q: Find the volume generated by revolving about Oy the area in the first quadrant bounded by the curve…

A: Plotting the given function :

Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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

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Q: Find the dimensions of the right circular cone of the greatest lateral area that can be inscribed in…

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Q: Find the volume of the torus that results when the region enclosed by the circle of radius r with…

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Q: Find the volume enclosed by the torusp = 4 sin().-

A: The volume is given by: V=∫∫∫dv In spherical co-ordinate dV=ρ2sin φ dρ dφ dθ

Q: Find the volume generated by revolving the area bounded by the parabola x2 = 4y and its latus rectum…

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Q: 8 Set up surface aenerated by revolving the given. Curve about the indicated axis, an integral for…

A: y=x3, 0≤x≤2, about x-axis

Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Calculate the second moment of area of a 4-in-diameter shaft about the x-x and yy axes

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

Q: Find the volume, if an area bounded by an asteroid I = cos t y = sin³ t ve y = -/I+x ,y-axis, and…

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Q: Find the volume of the cap of a sphere with radius R and height h using a triple integral. R.

A: Consider the following figure By Pythagorean theorem x2+y2=R2 ⇒x2=R2−y2

Q: Find the area of the surface generated by revolving the curve x = Osys2, about the y-axis

A: Given: The curve is x=y32, 0≤y≤2 about the y-axis The formula for find the area of the surface is…

Q: Find the area of the surface generated by revolving the region bounded by, 1 + 6 y 1<x < 3 16x4…

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