Compute the surface area of the cone with parametrization p(r, 0) = (r cos 0, r sin 0, r) where 0 < 0 < 2n, 0 < r < 1.

Q: Use cylindrical coordinates to evaluate the triple integral ||| E is the solid bounded by the…

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Q: Find the area of the region bounded by the curve defined parametrically by x = 4cos 2t, y = 4 sin 2t…

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Q: We consider a thin plate having the shape of the surface S parametrized by Ř(u, v) = v cos(u)i + v…

A: The equation of the thin plate is as given below. Ru,v=vcosui+vsinuj+uvk  and 0≤u≤4π 0≤v≤3

Q: The standard parametrization of the circle of radius 1 centered at the point (1, 0) in the xy-plane…

A: using the formula to determine surface area revolving to y axis S=2π∫abx(t)(dxdt2+dydt2)dt

Q: Find the moment of inertia of the solid formed by revolving about oy the area bounded by y2 = 2x and…

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Q: Use the triple integral in spherical coordinates to evaluate where G is bounded by yz-plane , x = /9…

A: image is attached.

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: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

A: See the attachment

Q: Use cylindrical coordinates to evaluate the integral 2²dV where E is the solid that lies within the…

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Q: Find the moment of inertia of the solid formed by revolving about oy the area bounded by * y2 = 2x…

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Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z &gt; 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z &gt; 0, by the cylinder x2 + y2 = 2y

Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

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Q: The surface area of the surface generated by revolving y =x³ , 0 Sx<1 about the x- axis is

A: Given : y= x3    ,  limit  0 to 1

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 3 cos t, y= 2…

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Q: Find the area of the surface generated by revolving the curve x = Vy, 0<y <4, about the y-axis.

A: We will use standard method.

Q: Compute the surface area of the surface segment parametrised by x(u, v) = u² cos v, y(u, v) = u² sin…

A: Given, xu,v=u2cosv,yu,v=u2sinv,zu,v=u2where 1≤u≤3 and 0≤v≤2π To find the surface area.

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: • This is a problem based on the applications of definite integral.  First we have to identify the…

Q: Find the moment of inertia of the solid formed by revolving about oy the area bounded by y2 : = 2x…

A: The solution are next step

Q: !! Evaluate the triple integral 2.rz dz dy dx by changing in to cylindrical coordinates. 0 0

A: Transformation from Cartesian (x, y, z) to Cylindrical coordinates:

Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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Q: Compute the surface area of the cone with parametrization p(r, 0) = (r cos 0, r sin 0 , r) where 0 <…

A: Differentiate the function φr,θ=rcosθ,rsinθ,r partially with respect to r and θ, to compute φr×φθ.…

Q: Find the area of the surface generated by revolving the region bounded by, 1 1syss 16y4 y6 1<y< 5 6.…

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Q: Find the area of the surface generated by revolving the curve x = 2 cos θ,       y = 2 sin θ,   0 ≤…

A: If x=f(t), y=f(t) then surface area is, About x axis: S=2π∫abydxdt2+dydt2dt About y axis:…

Q: Find the line integral with respect to arc length (5x + 3y)ds, where C is the line segment in the…

A: Given integral∫C5x+3ydswhere C is the line segment in x-y plane with the end points P(5,0) and…

Q: Let C be the curve intersection of the sphere x'+y+=9 and the cylinderx+y° =5 above the xy-plane,…

A: To Evaluate: ∫CF·dr Using Stoke's theorem. where F→=&lt;2yz,5xz,lnz&gt; and C is the curve of the…

Q: Find the area of the surface generated by revolving y = Vx +1 from r = 1 to x = 5

A: The objective is to find the area of the surface generated by revolving y=x+1 from x=1 to x=5.

Q: Find the moment of inertia about the x-axis of a thin plate of density d = 1 gm/cm2 bounded by the…

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Q: . Calculate the flux integral fF.n ds, where C is the positively oriented circle of radius 1…

A: Given function is, Fx,y=x,2y The formula for calculating the flux of the integral ∮F·nds is,…

Q: What is the volume of the solid rotated about the x-axis under the curve y = 2x -1 from x = 1 to x =…

A: Volume by disk method: The volume of a shaded region bounded by two curves over the interval [a,b]…

Q: Determine the area of the surface generated by revolving y=x³ on (0,1), about the x-axis.

A: The given curve is y=x3  on 0, 1 about x-axis. This implies that,…

Q: Convert into cylindrical coordinates. Tis in the First Octant bounded by Z = 3√x²+4/² Z SS S dy √x²…

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Q: Set up the surface integral for upward Flux of the upper hemisphere of radius = 5 (z20) such…

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Q: Find the area of the surface generated by revolving the given curve about the indicated axis. 1. x =…

A: Consider two parametric equations and with . Then the area of the surface obtained by rotating…

Q: Find the area of the surface obtained by rotating the given curve about x-axis. x=cos (t),…

A: We have to find the area of the surface obtained by rotating the given curve about the x-axis. x=cos…

Q: Let S denote the part of the cone z = Vx2 + y? that lies between the surfaces z = 2 + sin(xy) and z…

A: Given : S denotes the part of the cone z=x2+y2 that liesbetween the surfaces z=2+sinxy and…

Q: calculate the surface area of the solid obtained by rotating the curve over the g.iven interval…

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Q: Find the average of the function f(r,0)=r sin(0/2) over a disk of radius R centered at the origin.

A: Given function: f(r,θ)=r2*sinθ2Disk description: radius=R0 and center at the origin To find: Average…

Q: Find the area of the surface generated by revolving the given curve about the yy-axis.…

A: Given curve is, x=25-y, -1≤y≤0 Now, differentiating with respect to y we get,…

Q: Evaluate the line integral Jxy + z)ds where c the arc of circle x + y = 4, z= 0 from (2, 0, 0) to…

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Q: Compute the scalar line integral xy ds where C is the part of the circle of radius 3, centered at…

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Q: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

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Q: The volume of the solid generated by the curve y = e², between z = 2 and z =7 about the I - azis is…

A: Given curve is y=e-x  x=2 and x=7 about the x axis find the volume

Q: Express the double integral || (x +1)dA, where 2 is the region in the upper half- plane (i.e. y20)…

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Q: Given the scalar functionf (x, y) = 2xy, calculate the line integral along the ellipse curve+ 1 from…

A: Here we have to find the value of the line integral of function f(x,y)=2xy alone the ellipse…

Q: use spherical coordinates to find the moment of inertia about the z-axis of the solid of uniform…

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Q: Compute the surface area of the cone generated by revolving the curve c(1) = (1, mt) about the…

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Q: Given the scalar functionf (x, y) = 2xy, calculate the line integral along the ellipse curve+ 1 from…

A: Given: f(x,y)=2xy From the point (3,0) hesta (0,2)

Q: D Find the area of the surface generated by revolving the region bounded by, 1 1 <x < 5 4 8x2 about…

A: In the question we have to find area of the given function.

Q: Find the area bounded by the parametric curve x=cos(t),y=et,0≤t≤π/2, and the lines y=1 and x=0.…

A: Given: x=cost,y=et, 0≤t≤π2