b-Two curves x = 0 – sin 0, y = 1 - cos 0 are rotated around the y-axis. Calculate the area of the resulting surface over interval [0,2n]

Q: 9. The arc of the parabola y = x² from (0,0) to (1,1) is rotated about the x-axis. Find the area of…

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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. - 10 10 cos (0),…

A: Find the derivatives with respect to θ

Q: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y = 2r² (0 <t s…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: Find the surface area of the solid by rotating the curve x = cos3θ , y = sin3θ for θ = 0 to θ = π/2…

A: Given that the curve x=cos3θ       y=sin3θ         0≤θ≤π2 To find the surface area of the solid by…

Q: 3. Find the area of the surface generated by revolving about the y-axis the part of the curve y = x?…

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Q: x In(x) 5. Find surface area generated when the curve y =- 4 for 1<x<2 is rotated about the 2…

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Q: cos(3t), y = 6+ sin(3t) on 0 <t <

A: Please see the explanation below

Q: Find the area of the surface generated by revolving the curve x= cos (3t), y = 5+ sin (3t) on 0sts,…

A: Suppose parametric curve rt=xt,yt for a≤t≤b are revolving about the x-axis then surface area…

Q: Find the area of the surface obtained by rotating the curve x = 6 cos 0, y = 6 sin³ 0, 0< 0 <n/2 %3D…

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Q: 3. (8.3) find the area of the surface obtained by rotating the curve y = v4- x2, -1<x < I about the…

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Q: Find the areas of the surfaces generated by revolving the curves about the indicated axes.x = cos t,…

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Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by ro the cosine…

A: I have solved b part as asked.

Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by rotating the sine…

A: Let's solve area of surface.

Q: 9) Find the area of the surface generated by rotating about the y-axis y = x' between (0,0) and…

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Q: 12. Find the surface area for the surface of revolution formed by revolving the curve y = v4 – x?…

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Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = a cosº…

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Q: Calculate the area of the surface formed by rotating the curve r = 2a cos 0 around the line 0 = pi/2

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Q: cos(2t), y = 4+ sin(2t) 0 <t< on 2

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Q: Find the area of the surface generated by revolving the curve about the given axis. x = 2 cos(0), y…

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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: Sc F. dr where F(x.y) = (3x² – 4v)i + (27 + cos(,³))j

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Q: 3. Find the area of the surface generated by revolving the curve y = 2/x ,1Sx<2, about the x-axis(as…

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Q: 5) Determine the area of the surface obtained by rotating the arc y = Vx –1 around the x- axis from…

A:

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 6 cos(e), y…

A: Solution

Q: Find the total distance traveled by a particle along the curve given in parametric form x=sint -t…

A:

Q: 36. Find the area of the surface generated by revolving the para- metric curve x = cos² 1, y = sin?…

A: Definition used -                               Area of the surface generated by revolving the…

Q: Sketch the regions enclosed by the given curves. y = 2 cos(5x), y 2 sin(10x), x = 0, x = 1/10 2.0…

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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: 3. Find the surface area generated by revolving the curve y = 2+ cos 0, x = sin 0 ; 0 <O< 2n about…

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Q: Use Green's Theorem to evaluate the line integral. (e-x²12-v) dx + (0-1²/2 + x) ay dy C: boundary of…

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Q: Find the area enclosed between the parametric curves x=2t^2 + 6 y=e^-5t and x-axis for t greater…

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

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Q: Find the area of the surface obtained by rotating the given curve about the x-a T x = 5 cos (0), y =…

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Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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Q: 1. Find the area of the surface generated by revolving the parametric curve x=r cos 0, y = r sin 0…

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Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

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Q: 3) Find the area of the surface that results from rotating the curve Y = sin MX, 0 s X < 1 about the…

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Q: 1(a) Find the arc length of the curve 2x = 3y2/3 over the interval from y=0 to y=1  1(b) Find the…

A: (a) The arc length of the curve 2x=3y23 over the interval y=0 to y=1 can be calculated by using…

Q: y = cos(x), 0 <x<

A: Consider the given surface whose area is required to calculate.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = square…

A: This is a problem related to find area of the curve using integration. Please use below method to…

Q: Consider the polar curves C2 :r = 4 cos 0 and C3 : r = 4 sin 0. %3D (a) Determine the slope of the…

A: C2: r=4cosθ       red colorC3: r=4sinθ        green color

Q: 8. Calculate the area of the region within the ellipse x2/a² + y²/b² = 1 parameterized by x = a cos…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

A: The solution are next step is

Q: the surface area of a .17 rotating the curve y = x power 3 around the x - axis between the points…

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Q: 3. Consider the surface sin (xy)+ cos (xz)+sin ( yz) =1. Find an equation for the tangent plane to…

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Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: Find the area of the regions bounded by the parametric curves and the indicated values of the…

A: We will find the area.

Q: 2. (a) Find the exact surface area that is generated by revolving the portion of the curve y = x²…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.