Let C be the curve y 14 7Va for 2.3 < ¤ < 3.7. 13 12 to 구 Find the surface area of revolution about the x-axis of R. 3.7 | f(x) dæ where Surface area - 2.3 F( x ) - 3.7 Now integrate to find surface area f(x) dæ = 2.3

Q: Let C be the curve y=8√x 3≤x≤4.3 Find the surface area of revolution about the x-axis of R.

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Q: 7. Let C be the curve y = 3x for 0 <x S 1. 0.5 Find the surface area of revolution of C about the…

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

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Q: ) Find the gavea d the region encleSed by the line x-In3 and the curves y= ex and %3D y= ex

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A: Introduction: To determine the parametric areas, one must compute the area under the mathbbR2R2…

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Q: The area bounded by the curve z 4y+7, the y-ax y =0 and y 2 is dy3D O 18 22 11 O 15

A: Area bounded by the curve can be calculated as

Q: 2/ Find the area of the region enclosed by the curves y=lx) and 0on the interven-4] A3 B. D, IS

A: Given: Area enclosed by y=|x| and y=0 on the interval [-1,4]

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…

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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.

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A: Use the formula for the surface Area when a parametric curve rotated about y-axis.

Q: 5. Do the following tasks using Mathematica. x = Y 4x + y? = 12 (a) Plot the curves in a single…

A: NOTE:- As posted multiple independent questions, we are answering only first question as per…

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Q: 16. Compute the surface area of the surface obtained by revolving the given curve about the…

A: To compute the surface area of the surface obtained by revolving the given curve about the axis x =…

Q: Evaluate the integral ∫Cydx−xdy over the curve C parameterized by r(t)= (cost,sint), 0≤t≤π2.

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Q: Find the surface area of revolution about the x-axis of y = 2x +7 over the interval 1 < x < 4 O O us…

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Q: An integral expression for the area of the surface generated by rotating the curve y=√x, 0≤x≤ 1…

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Q: 9. Find the area of the region enclosed by the curve x = y? – 4y and x = 2y – y². (Hint: integrate…

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A: We will find region bounded by given curve to apply Green's theorem

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A: We have to find the surface area of revolution about the x-axis

Q: 3. Suppose the curve x = t³ – 9t, y = t+3 for 1 <t < 2 is rotated about the x-axis. Set up (but do…

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Q: Suppose f(x) is a differentiable function. State the formula that determines the area of a surface…

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Q: Let f be positive with a continuous derivative. Then the surface area obtained by rotating about the…

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Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

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Q: 3. Recall that the error in using the Trapezoidal rule to estimate | f(x) dx is M (b – a)³ |Fr| <…

A: As per our guideline we supposed to answer only first question , kindly repost other as next…

Q: 10. Find the surface area of the surface attained by revolving the curve y = f(x) =x' around the x-…

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Q: x Inx - Find the area of surface obtained by rotating the curve y= 4 - for 1<x<4 about the x – axis.…

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Q: Find and shade the area to the left of cach positive z value. Given Curve 1. C-0.9s 2. z= 1.47

A: As per company guidelines I solved exactly three subparts of the question.thank you

Q: Let S be the surface area generated by revolving the curve y = Vx, 2 < x < 12 about the x- axis.…

A: This formula is used

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Q: Q3 Knowing that: $. (2xy – x?)dx + (x + y²)dy [оСх + y?) д(2ху — х?)| dxdy, дх ду R where C is the…

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Q: (ii) Calculate the area under the curve defined parametrically as x(t) = t² +2t y(t) = t³ For t=0 to…

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Q: The surface area obtained by rotating the curve y = e*, 8s xs 10 about the x-axis is Your answer:…

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Q: 1sxse about the line x = 46 is The area of the surface obtained by rotating the curve y = 12 O 21 dx…

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Q: Let C be the curve y = 5 for 1 <r < 4.6. 11 10 7 4 Find the surface area of revolution about the…

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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: Evaluate the line integral fe 3y dx + z? dy + (25 - x) dz over the quarter of the circle of radius 5…

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Q: 343 2 1. y = x² - 9 and y = x + 3 (Answer: 6 s. u.)

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Q: Let C be the curve y = 6/a for 1.6 < ¤ < 3.8. 12 10 4 2 Find the surface area of revolution about…

A: The curve is given as : - y=6x  for   1.6≤x≤3.8   We need to find the surface area of revolution…

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Q: (b) Use Green's Theorem to evaluate ſ. 3ysin(x)dx + 5xdy where C is the boundary of the region…

A: Solution:Given∫c3y sinx dx+5xdyFormula:∫cPdx+Qdy=∬ ∂Q∂x-∂P∂y dA

Q: Find the area bounded by the line y=4 and the curve described parametrically by: x(t) =…

A: Given: y=4x(t)=t-1t,    y(t)=3t+1tSince y=4,  y(t)=3t+1t ⇒ 3t+1t=4⇒3t2-4t+1=0⇒3t2-3t-t+1=0…

Q: The volume, when the curve y = √3+ x2 from x = 0 to x = 4 is rotated about x-axis is O100m cu units…

A: Given:    y=3+x2 from x=0 to x=4  Volume of the curve V=π∫abfx2dx

Q: Express the area of the surface obtained by rotating the curve y=in cse(2x) between x= and x= about…

A: surface area about y axis S=∫ab2πxds ....(1) where  ds=1+(dydx)2dx

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: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

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