Q2. Let f(x)= In(cos x) (i) Find the arc length (ds) of the function (ii) Determine the surface area of the solid obtained by rotating the function over the interval 0sxs", about the x-axis. 4

Q: Calculus question in photo

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Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x' from (0,0) to (1,1).…

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Q: For the function f(x) = e* + e*, prove that the arc length on any interval has the same value as the…

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Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Find the arc length of the curve y(x) for the interval 1 < x<7 where y = S* Vt² – 1 dt +2.

A: We find arc length of given curve

Q: Use the Taylor’s formula to find a cubic approximation of f(x, y) = ex cos y near the origin.

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Q: Evaluate the integral / (2x + 15y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

A: We need to evaluate the integral ∫C(8x+12ydx+(9x-y)dy along the parabolic arc y=x2. from (0,0) to…

Q: The integral that represents the arc-length of the curve y = In x, x E [2,3] is: A) 3 Vx2+1 dx. B)…

A: Please refer to the image below

Q: Express the arc length of the curve y = x 4 between x = 2 and x = 6as an integral (but do not…

A: Given y=x4 between x=2 and x=6

Q: Evaluate the integral / (2x + 9y)dx + (6x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: Evaluate the integral arc y = x² from (0,0) to (1,1). NOTE: Enter the exact answer. (2x + 18y)dx +…

A: Given integral is ∫C(2x+18y)dx +(3x-y)dy We have to evaluate given integral along a parabolic arc…

Q: Which is the following integrals does NOT represent the arc length of f(x) = x²on the interval -3…

A: given function :

Q: Evaluate the integral / (4x + 18y) dx + (27x – y)dy along the parabolic arc y = x? from (0,0) to (1,…

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Q: Consider the curve segments: $1: y = x from x =- to x = 2 and S2: y = Vxfrom 1 x =- to x = 4. 4. Set…

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Q: 4. Evaluate the line integral 6. x²y dx – xy² dy where C consists of the arc of the circle 16 = x² +…

A: Given equation of circle is  x2+y2=16x2+y2=42 radius is 4 We have to calculate line integral ∮ cx2y…

Q: (a) Set up an integral for the length of the arc of the hyperbola xy = 1 from the point (1,1)  to…

A: Part (a)

Q: 1) The arc length of the curve y = f(x) Over the interval asx<b is Length = +(s'x)}° de Approximate…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Consider the curve segments: S1: y = x from x = 1 to x = 2 and 1 S2: y = Vx from x =to x = 4. Set up…

A: Let's find.

Q: Consider the curve segments: 1 - to x = 4 and 4 1 X = -to x = 16. 16 S1: у %3D = x² from x = S2: y =…

A: Given that:

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

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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…

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Q: Evaluate the integral | (6x + 3y)dx + (9x – y)dy along the parabolic arc y = x? from (0,0) to (1,…

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Q: =) Sketch the curve y-x. b) Use the following formulas to set up two integrals for the arc length…

A: for the graph, the second option is correct

Q: The arc-length of the curve y= :/ Vcos(31) dt , for 0<x<- is given by which of the following…

A: For the given statement

Q: x? In x Find the arc length of the curve y= f(x)= 4 on the interval [1,2]. 0.1

A: We will use integration to find arc length

Q: Evaluate the integral (2x +3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

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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: 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: Consider the curve segments: 1 $1: y = x from x =to x = 3 and 4 S2: y = Vi from x = to x = 9. 16 Set…

A: Please refer the attached image for complete solution. THANK YOU.

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: Evaluate the integral [(4x + 15y)da + (6x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

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Q: Find the arc length of the curve y(x) for the interval 1 < x <7 where y = S" vt2 – 1 dt +2.

A: We can use the concept application of derivative in order to solve the given problem.

Q: Use Simpson's Rule with n = 4 to estimate the arc length of the curve y = 0.5e-2x, 0 <x < 2. L = Só…

A: The curve, y=0.5e-2x, 0≤x≤2.

Q: 5. Compute the arc length of the curve e f (x) =1+In(cos(x)) over the interval from x=0 to 4

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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: 2.a) Apply the Trapezoid and corrected trapezoid rule, with h = 1, to approximate the integral 1 dx…

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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: The arc length of the curve defined by the equations x(t) 10 cos(11t) and y(t) = 3t for 1 <t< 5 is…

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Q: Evaluate the integral (4x +9y)dx + (9x – y)dy along the parabolic arc y = r from (0,0) to (1,1). (4x…

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Q: Which integral expresses the arc length of y= In(cos x) from x = n / 6 to x = T |4? | sec(x) dx |…

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Q: The arc-length of the curve y= / ycos(4t) dt, for 0<x<- 8. 0. is given by which of the following…

A: we have to find the length of the curve

Q: The integral dx represents the arc length of which curve (for 0<x<1) ? + y = 6 O y = e6x O y = e3x y…

A: Given that The integral represents the arc length of the curve over the interval [0,1] To find the…

Q: x = e'; y = 2t3. Set up the integral to compute the arc length from the point (1, 0) to (e², 16).…

A: The parametric equation is given by x = et; y = 2t3 To evaluate: The integral to compute the arc…

Q: For the function f(x)=1/4e^(−x)+e^x, prove that the arc length on any finite interval has the same…

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Q: Evaluate the integral | (2x + 9y)dx + (21x – y)dy along the parabolic arc y = x from (0,0) to (1,…

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Q: r(t) = (e' cos t)i + (e' sin t)j + e'k, -In 4 < t< 0

A: rt=et cost i+et sint j+et k,   -ln4≤t≤0 Differentiating with respect to t, we get vt=drtdt=ddtet…

Q: Q2// Find the resulting volume of the curve y = sin x cos x rotation about the x-axis if x=0, x=/?

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Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1,1).…

A: Given

Q: Consider the curve segments: S1: y = x from x =- to x = 2 and S2: y = 1 Vxfrom x = to x = 4. Set up…

A: I am going to solve the given problem by using some simple calculus to get the required result.