Question

MA112 2 Name.. Student ID.................. Instructions: Answer each question to the best of your ability. You MUST SHOW ALL WORK for full credit. Clearly indicate your final answers. Good luck! 1. Let n be the last digit of your student ID. Consider the vector field 3.02 - } (x, y) = 6x In(y)i + -) 3, for y>0 Y | 7 di is independent of path in a simply connected (n+1.e) 1.1 (3 points) Determine whether (n+1,1) region containing the points (n +1,1) and (n +1,e). (n+1,e) 1.2 (6 points) Use the Fundamental Theorem of Line Integrals to evaluate (n+1.1) Solution | 7. dr.

Answer 1

Given F (2,y) = 6x ln (y) +(3x² - 1) D Now (htle) in ht),1) to check if s rodre is independe el pole [ Condny do 32² - 1) dy / Fidy dn t (3n² y p. 60 ap oy y and do on Я on since al do on a fisa conservative vector field. dy & line intergalis pa the independent

Now second part by fundamental theorem of line integral

Entige) 62 dny dnt ( 3 22 14 dy c; (int))) It is anexact differential equations. (nt), e) d (13n2-1) iny) (ht) (+1, (3x2-1) any 11 (n+E, D) 6( n + 1) (3 + 1)2 -1) xo ri 3n+² -1