
) Evaluate Se Fodr F- axe'i + xpe's Ć consits of y=x² from (0,o) to (1,1)...
Evaluate & Fodr, where F(x, y, z) = (y² -2 2,5x) and C: 714) =<t", t, -tº), -15ts 1.
9. Evaluate the “vector valued” line integral 1.Podr Fodr where F(x, y, z) = (x, y, zy) TT and C is given by r(t) = (sint, cost, t), with N » 4. u sta
ScF.dr, where F = 2cevi+reyj and C consists of the curve of y = r² from (0,0) to (1,1) followed by the line segment from (1, 1) to (3,2).
Evaluate the line integral of the function f(x,y)= (x+y2)/(sqrt(1+x2)) over the curve C: y=x^2/2 ; from (1,1/2) to (0,0)
Evaluate // e-(x+vº)dA where D = {(x,y): x2 + y2 <1,1 20, y 2 0}.
Question 12 10 pts (10) Evaluate fc F.d7, where F =< y- cosy, asiny > and the closed curve C is the quarter-circle given by x2 + y2 = 9 from (0, 3) to (3,0), followed by the line segment from (3,0) to (0,0), followed by the line segment from (0,0) back to (0,3).
4. Use Stokes' Theorem to evaluate Fodr where F =x' i -4:+ xy k and Cis is the circle of radius 1 at x = -3 and perpendicular to the x-axis. Chas a counter clockwise rotation if you are looking down the x-axis from the positive x-axis to the negative x-axis. See the figure below for a sketch of the curve.
5)Evaluate f (x2-y)dr + (y2 +x)dy along a) a straight line from (0.1) to (1,2), b) straight lines from (0,1) to (1,1) and then from (1,1) to (1,2), c) the parabola z t,y 1
Evaluate Sc f(x,y)ds where is the curve y = x for 0 < x < 1 and the surface is f(x,y) = 1 + 9xy Select one: 14 a. 5 O a. V O b. O c. 18 13 O d. 1
13. (10 points) (a): Find the line integral of f(x, y, z) = x+y+z over the straight-line segment from (1,2,3) to 0,-1,1). (b): Find the work done by F over the curve in the direction of increasing t, where F=< x2 + y, y2 +1, ze>>, r(t) =< cost, sint,t/27 >, 0<t<27.