Evaluate the integral |xy dx – z dy + 8z dz where C is the curve with parametric equations x = 2t, y = cos t, z = sin t for 0

Q: Evaluate the line integral -y dx + z dy + 2x dz, where C is the helix by 7(t) = (cos t, sin t, t),…

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Q: Evaluate the line integral y dx +xdy; C is the curve x = 4t, y = t³ – 1, 0sts 1. Jy dx + x*dy (Туре…

A: Consider the provided question,

Q: Evaluate the unoriented line integral (22 + y° + z²) ds (2x² along the parametric curve a : [0, 1]…

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Q: Calculate the integral xy² dy – x²y dx where L is along the curve x + y ² = a? (a > 0) in a…

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Q: Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: One-form ω=xydx+12ydy and the parametric curve α:0, ln2→ℝ2 defined by α(t)=e2t, e-2t. To…

Q: Given the integral representing the length of the parametric curve x = t,y=t", 0 < t <1 A dt [4¢ + 9…

A: Length of parametric curve , L= ∫abdxdt2+dydt2 dt

Q: Which of the following integrals represents the length of the parametric curve x = t -t, y= t2, 1<t<…

A: Here we use the formula for find the length:

Q: Calculate the integral of f(x, y, z) = 3x² + 3y² + zª over the curve c(t) = (cos t, sin t, t) for 0…

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Q: Use Green's Theorem to evaluate the line integral f(e*c - 2y)dx+(5x+ev* dy, where C is the 15. 2cos:…

A: We need to find integral.

Q: Compute the line integral f 2xy dx + x2 dy along the following curves. (a) C1 along the circle x2 +…

A: A detailed solution is given in steps 2 and 3.

Q: Evaluate the line integral along the curve C. 3xy ds; C is the quarter circle r(t) = (cos t, sin t)…

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Q: Calculate the integral (x – y) dx + (x + y) dy I = x2 + y2 where L is along the curve y = cos x,…

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Q: Evaluate the line integral / V(ry + xz + yz) · dĩ over the curve F(t) = (t, 2t, 3t) for 0 <t < 4…

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Q: Evaluate the line integral for the given curve C. S-ds, C: r(t)= (t',t*),1<t<2 cy ||

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Q: Calculate the integral of f(x, y, z) = 7x² + 7y² + z³ over the curve c(t) = (cost, sin t, t) for 0…

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Q: Let f(x,y) = x 3 + y 4  + sin(2x+3y) . Determine the line integral of f(x,y) with respect to arc…

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Q: Evaluate the integral [(e' - y)dx + (sin y +x)dy using Green's theorem where C is 16 bounded by y =…

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Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

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Q: Give the integral representing the length of the parametric curve x=t^3, y=t^4, 0≤t≤1.

A: Given: A parametric curve:   Now the length of the parametric curve is given by the formula:

Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t > 0. COS So r(t)dt Compute the integral above.

A: ∫0πr(t)dt=∫0π&lt;t,3cos t,3sin t&gt;dt               =∫0πtdt i+∫0π3cos tdt j+∫0π3sintdt k…

Q: Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: ω=xydx+12ydy To find: I=∫αω  where α:[0,ln2]→ℝ2 with α(t)=(e2t,e-2t) ∴x=e2t,y=e-2t Now,…

Q: The area of the surface obtained by rotating the curve y = 1 I+ X, 1 <xse about the line x = 28 is…

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Q: Evaluate the line integral f, F . dr, where C is the curve given by F(t) = 3 cos ti+ 3 sin t j, 0<t<…

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Q: Calculate the integral I = | (2a – y) dx - (a – y) dy where L is the curve represented as x = a(t –…

A: (2a - y) = 2a - a(1 - cost) = a(1 + cost) (a - y) = a - a(1 - cost) = acost dx = a(1 - cost)dt dy =…

Q: Given the scalar function f(x,y)=2xy,calculate the line integral along the ellipse curve from point…

A: Given data:- The given curve is, x29+y24=1 The given scaler function is, f(x,y)=2xy t E 0,π/2

Q: Which of the following integrals represents the length of the parametric curve z = 1+e, y=ť, 3 <t<…

A: In order to know the length of the given parametric curve we will use the formula  where  -----

Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: Set up, but DO NOT EVALUATE an integral to compute the arc length of the curve given by the…

A: See below the answer

Q: Evaluate the integral c (xy+z^2)ds where c is the arc of the helix x=cos t ,y =sin t, z=t which…

A: To evaluate: The integral ∫c (xy+z2) ds where C is the arc of the helix x=cos t, y = sin t, z = t…

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A: Given line integral is,

Q: | 5y? dx +xy dy

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Q: Which of the following integrals represents the length of the parametric curve x =t+ cos(t), y =t -…

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Q: Set up an integral to compute the arc length L of the curve C: r(t) = (, 4t, v2t) %3D from the point…

A: I am going to setup an integral to compute the arc length of the given curve using the required…

Q: Integrate ƒ(x, y, z) =-2x2 + z2 over the circle r(t) = (a cos t)j + (a sin t)k, )  0&lt;=…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Green's Theorem:- To find the line integral of a function along a closed curve C…

Q: Evaluate the line integral F. dr, where F (x, y) = (3+2xy) i+ (x² – 3y²) j and C is the curve given…

A: Given problem:-

Q: Evaluate |(2y+cos x)dx + (5x+ sin y)dy along the positively oriented curve C. C is the boundary of…

A: We have to evaluate the integral ∫2y+cosxdx+5x+sinydy along the positively oriented curve C. Where C…

Q: Find the area under the curve for the parametric function defined by the equations x(t) = 5t, y(t) =…

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Q: Evaluote the live integral | (xZ+ y) ds along the curve c defined byき)=くターも,スセt,-スモ> ON Osts I -21…

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Q: Use Green's theorem to evaluate the line integral I of the one-form W = + æ sin? (y)) dæ + (x²…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y dx…

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Q: Evaluate the line integral Sp(xi+ yyj) · dr where D is the oriented curve shown below. (1,1) y = x²…

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Q: Let S be the surface parametrized by x = r cos 0 y = r sin 0 z = 30 where and 0<r< 4 Evaluate the…

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Q: Find the area enclosed by the given parametric curve and the x-axis. x = 4 sin(t), y = sin(t)…

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Q: Evaluate the line integral along the curve C. x² +y² ds, C is the curve r(t) = (2 sin 6t)i + (2 cos…

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Q: Evaluate the unoriented line integral +y² + z²) ds along the parametric curve a : [0, 1] → R³ with…

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Q: Evaluate the line integral ∫C -y dx + z dy + 2x dz, where C is the helix r(t) = (cos t)i + (sin t)j…

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Q: Find the area under the parametric curve x= 2(t + cos t), y=2(1 - sin t) from t=0 to t= pi.

A: We have to find the area under the parametric curves whose equations are : x=2t+cos ty=21-sin t…

Q: Compute the line integral [(yze²v² + y² + 2 − 2x) dx + (xze²v² + 2xy) dy + (xye²³² +x+32²) dz, where…

A: We have to compute the line integral ∫Cyzexyz+y2+z−2xdx+xzexyz+2xydy+xyexyz+x+3z2dz, where C is the…

Q: Set up an integral to compute the arc lengthL of the curve C: r(t) = (, 4t, v2t) from the point (0,…

A: Arc length