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

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: b) The area bound by the curve y = 2x + 1 and the y-axis is rotated about the y axis between y = 2…

A: We need to calculate the volume.

Q: Find the surface area of the solid obtained by y=2x, 0sx58revolving around the x-axis

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Q: 2. Find the volume of the solid lying under the elliptic x2 paraboloid + 4 y2 +z = 1 and above the…

A: The elliptic paraboloid can be expressed as z=f(x,y) where fx,y=1-x24-y29. We have to notice that…

Q: 39. Find the volume of the solid lying under the elliptic paraboloid x²/4 + y²/9 + z R = [-1, 1] ×…

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Q: Find the surface area of ​​the solid intersection of the cylinders x² + z² = 1 and y² + z² = 1

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

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Q: f(x) = x³, with 0 < x < 1

A: We know, the surface area of the solid that is obtained by rotating the graph of y=f(x) about the…

Q: 1(b) Find the surface area generated by revolving the portion of the curve y x2 + 1 between x=0 and…

A:

Q: 16 The area under the curve 4y? (x2 + 1)3 was rotated about a line located to the left 9 of y – axis…

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Q: 2. Suppose you revolved the triangular region bound by the axes and the line 4x + 3y = 12 completely…

A:

Q: Find the surface area of revolution about the x-axis of y = 7x +7 over the interval 2 <x < 3

A: Given function,     y=f(x)=7x+7, 2≤x≤3f'(x)=dydx=7Here lower limit is 2 and upper limit is 3

Q: 4. Find the volume of the solid obtained by rotating about y ax[is the re[gion between y=x^2 and…

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Q: What is the volume of solid of revolution between the curves y=x+1 andy 0 around the x-axis on…

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Q: Find the surface area of revolution about the x-axis of y 4x +7 over the interval 0 < r<3

A:

Q: Find the surface area of revolution about the x-axis of y = 2x + 7 over the interval 0 <x <1

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Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x…

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Q: 1. Find the area of surface that is generated by revolving the portion of the curve y = V4- r2…

A:

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: 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: 10. Determine the surface area of the part of z = xy that lies in the cylinder given by x² + y² = 1.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: :- Find the volume of the solid between y = x+1 which obtained the curves y = (x-1)² and by rotation…

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Q: Find the surface area of revolution about the x-axis of y=4x+3 over the interval 2≤x≤5

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Q: 6. Find the volume inside the paraboloid z = 9-x² - y², outside the cylinder x² + y² = 4, above the…

A: Relation between rectangular and polar coordinate  x=rcosθy=r sinθx2+y2=r2θ=tan-1yxdxdy=rdrdθ

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

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Q: 1. Find the surface area of the solid obtained by revolving the curve y = √25-x from = 9 to x = 16…

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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 surface area of revolution about the x-axis of 5z +3 over the interval 1 < z < 2

A: y=5x+3 &amp; given interval 1≤x≤2As we know surface area of revolution abput x-axis from x=a to…

Q: 5. Find the volume under the paraboloid z = -x² – y², and above the cone z = -. -V#²+ y².

A: Given

Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

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Q: Find the surface area generated by revolving y=5x+2 about the x axis on the interval [0,6]

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Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

Q: f(x) = x², with 0< y < 4

A:

Q: 5. Find the centroid of the solid formed by revolving the area between the curves: y? = x and y = 2…

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Q: Find the surface area of revolution about the x-axis of y = 3x + 2 over the interval 0 < z <1

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Q: Find the volume of the solid that lies under the elliptic paraboloid z = y^2 + 8x^2 + 1 and above…

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

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

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Q: 12. Find the surface area of the solid obtained by rotating about the x-axis for 1sxs3.

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Q: Q6 Determine the surface area of the solid obtained by rotating y = V(2p – x)(2p + x), |x | < 2…

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Q: 1 (#3) Find the surface area for y = 3 on [0, 3] rotating on the x- axis.

A: Given an equation of a curve, The solid will form by rotating the curve about the x-axis.

Q: 2. Determine the area of the surface generated by revolving a given curve about a given axis. a.…

A: Formula to find the surface area by revolution helps to find the required surface area. Formula to…

Q: Find the surface area of revolution about the x-axis of y 6x + 3 over the interval 2 < x < 5

A: In the question the curve given is - y=f(x)=6x+3 , 2≤x≤5 We need to find Surface area of revolution…

Q: 8. Find the area of the surface of the region generated by rotating the curve y = x³ from x=0 to x=1…

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Q: 9. Find the area of the surface obtained by rotating the curve y = x',0sxs2 about the x-axis.

A: Given : y = x³, 0≤x≤2 about the x-axis

Q: Find the surface area of revolution about the x-axis of y = 2x + 6 over the interval 2 < x < 5

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-9x.

A: Given: y=e-9x and 0, 1 To find the surface of revolution about the x-axis on 0, 1 The formula for…

Q: 5. Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by…

A: Solution :- As per guidelines . I do first only.

Q: 2. Find the volume of the wedge cut from the 1-st octant in R³ by the surface z = 4-1 - y.

A: