Evaluate the line integral Vo• dr for the following function and oriented curve C (a) using a parametriIC C description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals. x2 + y? +z? TC C: r(t) = (cost, sin t, for 5 sts 3 p(x,y,z) = 2 Using either method, Vo dr = C (Type an exact answer.)

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

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Q: ind the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

A: To find the parametrization of the curve defined by the intersection of the two surfaces  and ,…

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A: We will find out the required value.

Q: 2) Find the work of F = (x² - y² -4,2xy) on the semi-circle of radius 2 centered at the origin…

A: ∮F·dr=∮x2-y2-4dx+2xydy             =∬S∂∂x2xy-∂∂yx2-y2-4 dxdy               By applying Greens…

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Q: Let the curve C be the line segment from (0, 0) to (3, 1). Let F = ⟨2x-y, 4y-x⟩ Calculate the…

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Q: Write the equation of the curve l_r(t) which traces the circle of radius (0,0,1) on the plane z=1.…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.