Question

Please explain in detail. Especially the parameterization as that is what I struggle with.

(1 point) Let F be the radial force field F(x, y) = xi+yj. Find the work done by this force along the following two curves, both which go from (0, 0) to (7, 49). (Use the Fundamental Theorem for Line Integrals instead of computing the line integral from the definition, as you did in the previous set. This way shows why the answers to the two parts must be the same - independence of path!) A. If C1 is the curve: x = t, y= t?, 0 <t < 7, then len F. dr B. If C2 is the curve: x = 7+2, y = 49t², 0 <t< 1, then Ver F. dr = |

Answer 1

xì ty3 22 if ya 코 Given F = F = x clearly f(x,y)= f(x,y) = x af hence the given vector field is conservative Work done is given by w=frod? along the curred whose F Safiche W (A) the Fundamental Theorem of Line Integral -S75.17 = f(Tetromal point onc) - fcemitend point C,:x=t, y=+², ost=7 Initial point = (on 0,0). Terminal points (7,49) ScFido - $(7,09) - $10,0) 72+ug? 0² 40² - ug (50) => 2 2 2 2 1225 49x25 (B) (q: 2= 7+2, Y = 49+2 ostal initial point = (010), Terminal points (7240) S ridi f(7,49) - $10,0) 1 225