Identify surface trace S in flat cut T. S: 182? + 9y? – 222 – 20 = 0 • T: z= 3

Q: Find the area of the surface that is generated by revolving the portion of the curve y= x² between x…

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Q: given ∫∫s (x2z) dS and S is the part in z = sqrt(x2+y2), which lies in x2+y2 = 1 calculate the…

A: we have to evaluate ∬Sx2zdS Now, we have z=x2+y2 ⇒z2=x2+y2∂z∂x=xz and…

Q: Calculate the line integral f (VS) ·d7 for f(r, y) = -cos(2r-y)+ yr + y? and the curve C given…

A: Solution

Q: Н.W Ql: Evaluate f y* dx - x'dy where C is the positively oriented circle of radius 2 centered at…

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Q: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: Find the following: The traces of the surface x2 + y? + 22 = 6 in the planes parallel to the…

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Q: Let C be the curve y 8ī for 1.5 < T < 3.6. %3D 16 15 14 13 12 10 Find the surface area of revolution…

A: the given curve is take derivative

Q: Given the surface x²y + y° z+ z?x = 38. Find the normal line and the tangent plane to the given…

A: A detailed solution is given below.

Q: nhuille Find the area of the rotaional L'C surface formed by rotating the part of the Curve given by…

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Q: Find the surface area generated by rotating the given curve about the y-axis. x = e' - t, y = 4e/2,…

A: *to find:- surface area, when rotating about y axis.

Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

A: We have to find

Q: (1– y°)dx+(x° +e )dy, where C is the boundary of the region between the circles x2 + y2 = 4 and x2 +…

A: Given integral, ∮C1-y3dx+x3+ey2dy Here C is the boundary of the region between the circles x2+y2=4…

Q: x = 3t – t, y = 3t2, 0<t< 1

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Q: Compute the surface area of the surface generated by revolving the curve c(t) = (t², t) about the…

A: Let x=f(t) , y=g(t) , a≤t≤b be a parametric curve. Then the area of surface generated by revolving…

Q: Given the curve x = a² - y² over the interval 0 ≤ y ≤ a/2, find the surface area of the solid formed…

A: Solution is given below:

Q: HW: Find the area of the surface generaled by revolving 1. Vy, 1 <y <8 about the x- axis. =DX

A: Find the attachment

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: Find the surface area generated b rotating the portion of the parabolic arc x = y^2 from x =0 and x…

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Q: Find the area of the surface generated by revolving the curve 6a ay y + 3a from y= a to y= 3a about…

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Q: Find the surface area of the solid obtained by rotating the curve 0 <y<1 about the y-axis. 3 a) c)-…

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Q: Find the area of the surface generated by revolving the curve 6a² xy = y + 3a from y= a to y = 3a…

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Q: Find the surface area generated by rotating the semi-circle x = 49 – y² be- tween -7 <y < 7 about…

A: Calculate surface area: S=∫-772πx1+dxdy2dy   =∫-772π49-y21+ddy49-y22dy   =∫-772π49-y21+-y49-y22dy…

Q: Use polar coordinates to find the integral 16 - x² - y? dx dy where R is the circle x? + y? < 4.

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Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: Q4:B/ Find the area of the surface generated by rotating the curve y = e", 0 < x<1, about the…

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Q: Find the surface area generated by rotating the given curve about the y-axis. x = et - t, y = 4et/2,…

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Q: Let C be the curve y = 6x for 0 S< 1.2. %3D 10 8. 7- 6- 5- 4. 2- 0.5 1 Find the surface area of…

A: Given: Let C be the curve y=6x3 for 0≤x≤1.2

Q: Find the area of the surface obtained by revolving the curve y=2/4=x, for 1<«<4, around the x-axis.…

A: Explanation of the solution is given below...

Q: Find the area of the surface generated by revolving the curve                             x = 4t, y…

A: If x = f(t), y = g(t) then surface area is 1) About x axis: A=2π∫abydxdt2+dydt2dt 2) About y axis:…

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y® +…

A: Given the curve, 8xy2 = 2y6+1,  1≤y≤2 we have to find the area of the surface generated by revolving…

Q: Find the surface arca of y = (1/3)r 10<x <1 revolved about the z-ax

A: Given: The equation is y = 13x3 , 0 ≤x≤1 revolved about the x - axis.

Q: Find the area enclosed by the polar curve r = 4e0.60 on the interval 0 < 0 < 4 and the straight line…

A: Explained below...

Q: Evaluate y*dx – a*dy, where C is the boundary of the region between the circles a? + y² = 16 and %3D…

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Q: x (t) = 3t – t3 y (t) = 3t2 %3D 0 st< 3

A: It is given that xt=3t-t3, yt=3t2 and 0≤t≤3. The  surface is rotated about the x-axis, thus the…

Q: Find the surface area generated by revolving the curve C:x(t) = 3t, y(t) = 2t (0 <t<1) %3D about the…

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Q: a) Find the surface area of the object obtained by rotating x = e2y , –1 <y <1 about the y – axis.

A: We have to find the surface area of the solid obtained by rotating the curve x=e2y about the y-…

Q: Use your grapher to find the surface's area 3) y = sinx, 0 s x < T/4; x-axis A) 5.46 numerically. B)…

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Q: Find the area of the surface generated when the given curve is revolved about the y-axis. y= (3x/3,…

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 15r If F(r) = and o is the surface (r – 3)? + y +z? = 49 oriented outwards, what is the value of F n…

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Q: Let C be the curve y = 5/a for 2.6 < a < 4.7. %3D 10 4 3 4. Find the surface area of revolution…

A: Function  y=5x for 2.6≤x≤4.7Formula→Surface area about x-axisS=∫ab2πy1+dydx2dx,  a≤x≤b

Q: 32. Find the area of the surface generated by rotating the portion of the curve y-2 from x= 0 to x =…

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Q: Find the area of the surface of rotation created y = /2x – x2; <a< by rotating this curve around the…

A: By using area of surface formula, we calculate the required area of surface.

Q: 5 st36. about x-axis is The area of the surface obtained by rotating the curve * = 3t, y = 48 – 4t O…

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Q: Determine which of the following gives the area of the surface obtained by revolving the curve y =…

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Q: ind the exact area of the surface obtained by rotating the curve about the x y = y1+ ex, OsxS8

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Q: 33. Find the surface area of the portion of the curve x²+y²4 from x₁=0 to x-2 when it is revolved…

A: We need to determine the surface area that is resulted when the portion of the curve: x2+y2=4 from…

Q: The area of the surface obtained by rotating the curve * = 3t, y = 67 – 4t 5 st s 6. about x-axis is…

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Q: The area of the surface obtained by rotating the curve * = 3t, y = 65 – 4t 5 st36. about x -axis is…

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Q: y = 2x C = ƏD D y = x?

A: We have to evaluate the integral ∫Cx-ydx+3x+tan-1ydy. Where C is the curve in the given figure.

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

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