Written HW 07 Gradient Fields Name Put your complete, final version of the solutions on this page to turn in. 5) Given the vector field F = and points P and Q with coordinates (a,0) and (-a,0) respectively. Sketch F and describe paths C1, C2, and C3 such that the line integrals over the three curves are 0, positive, and negative respectively. C. 4 xzasint yzacost a sacost yeasint bezacostut dy = -asintot do = - asindt dy = acostat fistst dyso Est 6 2 R Fids = ( 0) dat lady Fids = lacost ) ( acustadt ) Fleasint (-asintilt ) = 9240s 2+14 =a1 (1 + coszt )d+ = - 92sint de Card F. JS = 0 FUL = - a? ( 7+ cosZE ) E J Far = aTE A positive care) 6) a) In two different ways, find the value of the line integral . dr 7'9 negative where C is a path from (0,0) to (1, x /2) . (Hint: two ways exist that, algebraically, are neither difficult or complex. Be strategic and creative to find those solutions!) b) What is the interpretation of the numerical answer you got in part a) ? Give two possible meanings