I xy dx + 3xy dy where C is arc of parabola y = x from (3,9) to (1,1) 1.

Q: - Compute 5y dr a dy, where C is the arc of the parabola y = from (-2, 4) to (0, 0).

A: The line integral of the function with respect to x, y is solved using the formula…

Q: If y = Vx(3 – x)², show that- dy (3-х) (3-4x) Find the x coordinates of %3D dx all points on y =…

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Q: Find x²y°dx where C is the arc of the curve y? from (0,0) to (9,3)

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Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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Q: dy Differentiate parametrically to find dx in terms of t: x = 4t?,y= 2t3

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Q: ne if the curve (In t. t In t. 1) is tangent to the surface rz- uz? + cos Tu =1 at (0.0. 1).

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Q: I need to solve this question

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Q: Find the gardientoff at the indicatedpoint. frx,y)=D5sin x+Cos3y ;

A: Given: f(x,y)=5sinx2+cos3yπ2,0

Q: Find the arc length of the curvex (y² + 2)3/2 from y-0 to y=1

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Consider the curve defined by xy + y2 = 21 Determine dy/dx for this curve at the point (4, 3)

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Q: Find dy/dx and d²y/dx² at t = 2 for the parametric curve x = ½t², y = ⅓t ³.

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Q: Evaluate Iz = y", 2ry ) · d7 where C3 is the arc of the curve x = 3 – 2y that extends from (7, –2)…

A: we have to evaluate the following

Q: Starting from the point (3, 1, –1), reparametrize the curve x(t) = (3 + t, 1 – 2t, –1 – 2t) in terms…

A: We need to reparametrize the given curve in terms of arclength. The solution is given below.

Q: The arc length of y = 5++ from x = 1 to x : 2x (A) f 1+ (5 ++² dx +2 dx 2x (B) 2x2 (C) f1+ x2 dx 2x2…

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Q: Find the arc length of y = -6x + 2 on [2,5] (use calculus). %3D L = 1 + f'(x)² dx

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Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: x+ y dydx = Inß ху %3D Find B.

A: The objective is to find the value of beta.

Q: 5. (x²y + sin æ) dy, Cis the arc of the parabola y = r² from (0, 0) to (7, n²)

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Q: 1. Evaluate f(xy+2²)ds where Cis an arc of the helix C x = cost, y=sint, z = t which joins the…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: dy Find at t = T/4 for the parametric 2 sin(t), y = 3 cos(2t). curve x = dx2

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Q: 1. Find the arc length of the curve x = r=(y²+ 2)2 from y-0 to y-1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

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Q: fix+ (x+y) dx +(-3x²) dy L is arc curve x(t)=t5,y(t)=tº from (0,0) to (1,1

A: We will use  parametric curve to convert all variable in t and then integrate

Q: Differentiate parametrically to find X 1 t-1 y=t³+2 dy dx in terms of t:

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Q: Find the arc length of the curve y = (ex + e-x)/(2), 0 ≤ x ≤ 2.

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Q: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+1

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Q: A curve is written parametrically with x and y defined as functions of t: x=t2 +1, y = 4r° +3. Find…

A: Take the derivative of x and y with respect to t then use the formula for the arc length.

Q: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

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Q: (a) y = arctan (b) y = v1-x' arsin(x)

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Q: Q6 Evaluate S[(2xy – y? cos x)dx + (1– 2y sin x + 3x?y?)dy] where C is the arc of the parabola 2x =…

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Q: Find the arc length of the curve x=6y^3/2 from y=0 to y=3.

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Q: 4. Find the arc length of the curve x=y+y from y-1 to y-4

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Q: Starting from the point (2, –1, 2), reparametrize the curve r(t) = (2 – 2t, -1+ 2t, 2 – 3t) in terms…

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Q: Find the arclength of the curve z = 7 cos(3t), y = 7 sin(3t) with 0 < t< 12

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Q: Find the length of the curve x = 8 cos t + 8t sint,y= 8 sin t – 8t cos t ; 0 < t %3D -

A: The length of the parametric curve is given by  L=∫abx't2+y't2dt.

Q: Evaluate I C: arc on y = x³/2 from (0, 0) to (4, 8) (2x −y) dx + (x + 3y) dy.

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Q: 50. w = sin x + y²z + 2z, arcsin(t – 1), y = t³, z = 3 %3D

A: Since you have posted multiple question in this question which are not interlinked so I have solved…

Q: cos(u) dx. int_ccC [2x*cos(y) \ dx \ - | x^2 sin(y) \ dy] x? sin(u) dul if C is the curve x^4+y^4=1,…

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Q: 1. Find the arc length of the curve x = x=(y+ 2)2 from y-0 to y-1

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Q: Evaluate f. 2xcos[y] dx- x² sin[y] dy along the parabola y = (x - 1)2 from (1,0) to (0,1)

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Q: Starting from the point (-4, 5, 4) reparametrize the curve r (t) = (-4- 3t)i + (5 – 3t)j + (4 + 2t)k…

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Q: 3. Find the arc length of the curve æ = 5 + y3/2 between y = 0 and y = 2.

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Q: (2? – y) dæ + (y² + æ) dy] - where C is the parabolic arc Y = x2 from (1, 1) to (0, 0). Oo None of…

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Q: Consider the parametric equations x = t2 - 1 and y = t2 + 2t. (a) Find (dy)/(dx) and (d2y)/(dx2).…

A: Consider the parametric equations  x = t2 − 1 and y = t2 + 2t

Q: Find x dy + y dx, where C is the arc of the curve y = e² for 0 < x < 1

A: As per guidelines i can solve only first question

Q: ind the equation of the tangent line to right branch of the hyperbola == sec t, y= tant, 2 - sts at…

A: Topic:- application of derivatives

Q: dy Differentiate parametrically to find dx in terms of t: %3t2, y3 6t

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