Find the area of the surface generated by revolving the curve about the indicated axis. 8) y = 3x - x2, 0.5 sx s1.5; x-axis A) 37 8) B) T C) 4r D) 27

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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Q: Find the area of the surface generated by generated by revolving the curve about the r-axis. と4u:4+…

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Q: Find the area of the surface obtained by revolving the curve x=/y+1, for 1<y<, around the y-axis.

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Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

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Q: Evaluate ze dV, where E is the portion of the ball centered at the origin of radius 5, x + y+< 25…

A: Given Where E is portion of the ball centered at origin, radius 5 and lies in first octant. In…

Q: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: Find the area of surface that is generated by revolving the portion of the curve 9 – y² , – 2 < y< 2…

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Q: Find the area of the surface generated by revolving the curve y = Vx + 3, 4 < y <7 around the…

A: We have to find area of the surface . Given y=x3+3                                 4≤y≤7

Q: Use Green's theorem to evaluate 2y3 dx – x³y2 dy, where C is the positively oriented circle of…

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Q: Evaluate the line integral . xy ds, where Cis the top half of the circlex +y = 16.

A: The given integral is ∫C xy2 ds, where C is the top half of the circle x2+y2=16. To find: the value…

Q: s. y-- In x 1<X < 4 5. у 2 4

A: Formula for calculating surface area(S): S=∫ab2πyds                              where, ds=1+dydx2…

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: find the Volumae of soliel generated by revolving the region in the first quadsant bonended by y=X…

A: The volume of revolution generated by full revolution of the area A between the curves y1=f1(x) and…

Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

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Q: Find the area of the surface generated by revolving the curve y = cos(r), 0<aS5 about the r- axis.

A: The solution is given below in the next step:

Q: Determine the area of the surface generated by rotating around the "y" axis, the curve described by:

A: Here, the given parametric curve is: x=t33, y=t+1; 1≤t≤2⇒x'(t)=t2, y'(1)=1 Now, the surface area…

Q: Find the area of the surface obtained by rotating the curve y 4V7,0 < I < 5, along the r-axis.

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Q: Find the area of the surface generated by revolving the curve about each given axis. X = 3t, y = 5t,…

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Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: 5. plot x?-y?=z (Elliptic paraboloid) in 3D.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: The lateral (side) surface area of a cone of height h and base radius r should be Ar v? +h?, the…

A: Consider the provided question, Given the line segment, y=rhx,  0⩽x⩽h Differentiate both side of…

Q: Find the mZR in trapezoid QRST where QT||RS below.

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Q: Find the surface area of the cone frustum generated by revolving the line segment y-/2) + (1/2, 1…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = St, y= 9t,…

A: We have to find the surface area.

Q: Use Green's theorem to evaluate $ 2y3 dx – x3y² dy, where C is the positively oriented circle of…

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Q: Use Green's Theorem to evaluate the line integr y? dx + x • when C is the circle of radius 2…

A: Introduction: Let C be a positively oriented, piecewise smooth, simple, closed curve, and D be the…

Q: How many square units is the area of the surface obtained by rotating the curve y = V4-z, 0 <I<2…

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Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: Find the length of the circle of radius r defined parametrically by x=rcost, y=rsint,0≤t≤2π.

A: Here I am attaching image so that you understand each and every step.

Q: Under what conditions can you find the area of the surface gener-ated by revolving a curve x = ƒ(t),…

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Q: 63. х 3D 2t, у %3D 31, 0 <t < 3 (а) х-ахis (b) у-ахis

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Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: 35. Find the area of the surface generated by revolving the para- metric curve x = t, y = 21² (0 < 1…

A: Given: x=t y=2t20≤t≤1

Q: Find the area of the portion of the sphere x2 + y² + inder x2 + y? = 6y. %3D

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Q: Find the area of the surface of revolution generated by revolving C = {(x,y):x = y = 1- 2t, -1sts1}…

A: Given that C=x,y:x=-3+4t3, y=1-2t, -1≤t≤1 about the line x=2. The range of y is,…

Q: Find the surface area of a sphere of radius r

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Q: Let B be the ball with center at the origin and radius 1 SIS 4(z² + y² + z*)dv = B

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Q: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y= 21² (0 <…

A: Given: The curves,  x =t,  y = 2t2,   0 ≤ t ≤ 1 To find: The area of the surface generated by…

Q: For the conical surface 0 = 30°,0 <0< 21,0 <r< 2, the lateral surface area is what?

A: Sol

Q: The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 +…

A: Obtain the lateral surface area as follows.

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 2t, y = 3t,…

A: TO FIND THE AREA GENERATED BY THE REVOLVING BELOW SURFACES x =2t y =3t ,   0≤t≤9 FORMULAS USED (a)…

Q: Find the area of the surface generated by revolving the curve about each given axis. X = 9t, y = 9t,…

A: Solution

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

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Q: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O…

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Q: Evaluate the double integral. (8x – 6y) dA, D is bounded by the circle with center the origin and…

A: The given data is: ∫∫D8x-6ydA To evaluate the double integral.