ine Integral done by F over the curve in = C: r(t) = ti + tj + tk, 0 st s 1

Q: 6. Set up but do NOT evaluate Evaluate the line integral 2 curve (t) - (t", t), where 0sts0. L ds,…

A: Consider the given integral as ∫Cyxds, where C is the curve r⇀t=t4,t3 and 0≤t≤1. Note that, the line…

Q: (b) Use a theorem to find [F.dr. Which theorem did you use? Evaluate completely. Indicate the…

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Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

Q: The line integral P F.d7 can be evaluated using Stoke's Theorem where F = (2x, -3, 1) and C is an…

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Q: 5. √(x²y³ – √x) dy, C is the arc of the curve y = √x from (1, 1) to (4, 2)

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Q: Calculate . F · dr where F (x, y, z) = zi + xyj - y?k On the curve C r(t) = t?i + tj + vĩ k, 0<t <1…

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Q: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

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Q: Let f(r, y) = 1 + 2y² and F(x, y) = (-2y, 1). If C is the arc of the unit circle from (1, 0) to (0,…

A: We are given f(x,y)=x+2y2 ⇒fx=1 and fy=4y  x=cos t and y=sin t ⇒dxdt=-sin t and dydt=cos t Limits…

Q: In whatever way you see fit, evaluate the line integral L(10xy-3y+21x dx+ (15xy=+6xyz*)dy+ (15xy='…

A: given line integral ∫c10xy3z3+3y2z3+21x2z2dx+15x2y2z3+6xyz3dy+15x2y3z2+9xy2z2+14x3zdz   ...i…

Q: Evaluate ∮C (x + 3y)dx + ydy where C is the Jordan curve given by the graphs of y = e^x, y = e^−x…

A: ∮Cx+3ydx+ydy Where C:y=ex, y=e-x, y=e-1

Q: 2 f(t) = ( tv4t2 + 1, sin(t) cos² (t), t2 + 1

A: As you ask parts b and c. in part b we need to find the equation of the tangent line to the curve at…

Q: tangent plane and the normal line to the surface

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