1,2 is correct. 3 is wrong. I took x-5 = t to paremeterise. Consider the vector

Question

1,2 is correct. 3 is wrong. I took x-5 = t to paremeterise.

Consider the vector field: F(x, y) = (-y,x) Let C be the curve illustrated below, where A = (3,0), B = (5,0) and C = (5,24), and the third path from C to A is a section of the parpolic given by the equation: y = - 6(x - 5)2 + 24 For t [0,1] then r1(t) = Parameterisation of the first path For t [0,1] then r2(t) = Parameterisation of the second path Without using squarc-roots. For t [0,1] then r3(t) = Parameterisation of the third path Find the circulation of F over the whole curve C Answer is a Number

Explanation / Answer

since t is from 0 to 1

x = 5-2t

y = -6(2t)^2 + 24 = -24t^2 + 24

so r3(t) = (5-2t , -24t^2+24)

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