36. Find the area of the surface generated by revolving the para- metric curve x = cos² 1, y = sin? t (0 < t s a/2) about the y-axis. %3D

Q: Find the area of the surface swept out by revolving the para- metric curve x = 5 cost + 5t sin t y =…

A: Area under curve.

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 4 cos t, y =…

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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 surface area generated by revolving the curve x=y³²-y about the y-axis for 1≤ys 3/2 1/2 3

A: The surface area of any given object is the area or region occupied by the surface of the object.

Q: Show that the volume of solid formed by revolving one loop of the curve r2 = a? cos20 about the line…

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Q: 3 The arc length of the portion of the curve y=x2 with 0<x<4 is Osz9.0734 OSx 10.1938 s=7.7868 попe

A: We have to find the arc length of the portion of the curve y=x32 with 0≤x≤4.

Q: Q3/A/Find the surface area generated by rotating the curve y = cos h(x) about x axis for 0≤x≤1

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

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: (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: 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: 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: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

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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 x axis y=√x, 0≤x≤2( Note: I…

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Q: Find the area of the surface obtained by rotating the curve y = cos 2x, x is an element of  [ 0,…

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Q: 7. Find the surface area generated by revolving about the x-axis the curve y = 2(15-x)^1/2, from x =…

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Q: Find : ( 39 - Sincm) dx +(2x*) dy when C is the boundary of the limited area by curvess y= e* and in…

A: Given that I=∫c3y-sin x dx+2x2 dy                                   ……(1)   Boundary is given as…

Q: Where ds is calculated using the are length formulas from before (which ever is easiest)! 3. Find…

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Q: If the area enclosed by the curve x = 4 cos³ t and y = 4 sin t (wheret e R) is A then what is A?

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

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Q: Find the area of the surface generated when the indicated arc is revolved about the y-axis. y=x^2…

A: The given equation is y=x2 from x=0 to x=1. Find the area of the surface generated when the…

Q: Set up the definite integral(s) equal to the arc length of the curved defined by the parametric…

A: Use the formula of arc length in parametric form and simplify.

Q: 2) Use the surface area formula: S = 2ny 1+ () dx to find the surface area y = x, where 0 <x <1 of:

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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: 2.) Find the exact area of the surface obtained by rotating the curve about the x-axis y= cos(÷x) 0…

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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 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: Question 8 Calculate the area of the surface generated when the curve, y = Vx is revolved on the…

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

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

Q: Find the exact arc length of the curve 2xy = y² + 4 over the interval 2 ≤ y ≤ 4. Find the area of…

A: Given: 2xy=y2+4 over 2≤y≤4 to find the arc length of the curve and given the another equation is…

Q: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

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Q: 1. Find the equation of the tangent plane to the surface cosh [exp (x²y)] = Z y? at the point where…

A: We will find out the required equation of tangent plane.

Q: denote the square of the arc length differential over the surface of Z=xy. What do you need to do to…

A: The differential path length is: ds=dx2+dy2+dz2    =dx2+dy2+dxy2    =dx2+dy2+xdy+ydx2

Q: 10. Use a definite integral to find the exact area enclosed by the x-axis and the parametric curve =…

A: The given parametric curve is: x=2t3+1    and     y=2t-t2

Q: у 3 1 + sin х, 0 <x< т/2 y

A: The given curve is y=1+sinx and the limit is 0≤x≤π2 The Surface area is given by S=∫x2πy1+y'2dx or…

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 4 cos t, y =…

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Q: Find the area of the surface generated by eY + e -Y revolving the curve x = in the interval 2 In 5…

A: solution:-given curve x=ey+e-y2 in the interval 0≤y≤ln5revolving about the y-axisarea of a surface…

Q: Find the exact arc length of the curve over the interval 24xy = y* + 48 from y = 2 to y = 4 . Eind…

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

Q: Find the area of the surface generated by revolving the curve x = Vy, over the interval 8 sys 27…

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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: Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

A: We will draw region first, then find the area using double integral

Q: Find the area of the surface generated when the indicated arc is revolved about the y -axis. 6. y =…

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Q: Consider the curve y = 3 sin(2x), where 0 < x < T/2. Find the surface area when this curve is…

A: To find the surface area when the curve the is rotated about the x-axis.

Q: 1. (a) Find the exact area of the surface obtained by rotating the curve y = e* about the x-axis…

A: