Use Stokes' Theorem to evaluate L* + cos x) dx + (sin y + z²) dy + x dz where C is the closed curve parametrized by r(t) = (cos t, sint, sin 2t), t e [0, 27], with positive orientation. Hint: Since sin 2t = 2 cos t sin t, then the curve C lies on the surface z = 2xy.

Q: Use Green's theorem to evaluate line integral (9y – In(x2 + y2)) dx + (2 arctan( (2)) dy, where C is…

A: Green's theorem defines that : for ∮CPdx-Qdy there is an integral exists of ∫D∫∂Q∂X-∂P∂Y.dA Here,…

Q: 11. Use Stokes' Theorem to evaluate OF dr where F=(xz,e",y+z) on the curve that is the intersection…

A: The equation of curl is F=xz,ey,y+z. The equation of plane is 6x+3y+z=12

Q: Use Stokes' theorem to evaluate ∮C z2 ex^2 dx +xy2 dy + tan−1 (y) dz where C is the circle x2 + y2 =…

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Q: Evaluate the line integral (2 yi + (r- 2)j+ zyzk) · dr where C is the parametric curve r(t) = ti +…

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Q: x(t) cos(t), y(t) = 1+ sin(t), with 0 < t < 2n

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Q: Use Green's Theorem to evaluate the line integral. dx + (2 + x) dy -y2/2 - C: boundary of the region…

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Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.

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Q: Use a calculator or CAS to evaluate the line integral correct to four decimal places. x sin(y + z)…

A: find the explanation below

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: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Assuming that C is the counterclockwise oriented boundary curve of the unit square in the first…

A: It is an simple and easy question on vector calculus  Can be easily solve by use of green's theorem

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. O x2y dx,…

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Q: Consider the surface S shown in the gure and whose parameterization is given by: r(u, v) = (sin v,…

A: Consider the surface S shown in the gure and whose parameterization isgiven by: r(u, v) = (sin v, u…

Q: 3. Consider $ -y3 da + a?y dy where curve C is defined by the line segment from (-1,0) to (1,0),…

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Q: Evaluate ∫c (y+sin x) dx + (z2 + cos y ) dy +x3 dz where C is the curve r(t) = (sin t, cos t, sin…

A: ∫C y+sin x dx + z2 + cos y dy + x3 dz = ∫C y+sin x i + z2 + cos y j + x3 k (dx i + dy j + dz k)…

Q: Find an integral for the area of the surface generated by revolving the parametric curve about the…

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Q: 2/ MATH

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. x? from the origin to the (a) Find a vector parametric…

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Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. p x2y dx,…

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Q: Evaluate the integral |xy dx – z dy + 8z dz where C is the curve with parametric equations x = 2t, y…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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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: Suppose F(x, y) = -y sin(x)i + cos(x)j. Find a vector parametric equation for the parabola y = x²…

A: The solution is following.

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: 11. Let F = (-xy + xz²)i + (4xz + y²)j + e² k. Use Stokes' Theorem to calculate fcF. dr, where C is…

A: We have to find∫cF→.dr→.

Q: Verify the Green's theorem for the following integral $. sinydx + (x – cosy) dy where curve C is the…

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Q: 3) Use Stokes theorem to evaluate (| curl F-ndS. where F= (xyz, x, e" cos z), while S is a surface…

A: r(t) is the vector function for C, the curve around the base of the hemisphere (and therefore the…

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: Consider the curve C in R3 given by: F(0) = (sin 0 + 0) î+ (sin 0 – 0) ĵ+(-V2 cos 0) k, para 0<osa…

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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: Let F . F. dr, where Use Stokes' Theorem to evaluate C is the curve of intersection of the…

A: The given vector function: F→=&lt;xy,2z,3y&gt; To find ∫CF→.dr by using Stokes theorem. The Formula…

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: Verify the Green's theorem for the following integral O sinydx + (x – cosy)dy where curve C is the…

A: Answer

Q: Find the area under the curve for the parametric function defined by the equations x(t) = -2 cos t,…

A: Given: xt=-2cost  , yt=3sint , 0≤t≤π2 Formula used: The area under a parametric curve: A=∫abytx'tdt

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: The motion of a fluid particle is defined parametrically as follows, r(t) = sinh(t), and y(t) =…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = cos -х 0< x…

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Q: 3(b). FF as defined above, a misguided professor claims that for any losed curve C, F. dr = 0…

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Q: Compute the line integral | (yze*v= + y° + z - 2x) dr + (xze*# + 2ry) dy + (rye#"= + x + 32²) dz,…

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Q: Compute the surface area of the surface generated by revolving the astroid with the parametrization…

A: In this question, we find the surface of revolution by rotating the given parametric curve around…

Q: Show that the curve r(t) = (ln t)i + (t ln t)j + t k is tangent to the surface xz2 - yz + cos xy = 1…

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Q: Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along CoS the positively…

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Q: dr 2 +r² dt, 2 L = dz' (dt. dt, x = rcos(0) y = rsen(0).

A: Given a parametric curve x=rcosθ, y=rsinθ, z=z(t)  for a&lt;t&lt;b To show…

Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that,  F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: A) if F=2yi-zj+xk evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

A: Given x = costy = sintz = 2cost As F = 2yi-zj+xk Then F(x,y,z) = 2y , -z , x Thus F(x(t) , y(t) ,…

Q: Use Stokes' Theorem to evaluate , (x + y )dx + (2x – 3)dy + (y + z)dz over the boundary of the…

A: First we will learn about Stokes theorem little bit. If "F1 i + F2 j + F3 k" is a differentiable…

Q: 2). Use Stokes' theorem to evaluate the integral 6 F • dř for F(x, y, z) = (x – y)î + (y – z)ĵ + (z…

A: Formula: By Stoke's theorem we have ∮C F · dr¯  =∫t=t1t=t2 F¯(r(t))r'(t) dt, where r(t) is…

Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F =xi+ 5xj +zk…

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