M225Spring 2009Quiz 11Name:This is a group quiz, so you should speak to your neighbor(s). You may use a calculator,your notes and/or the textbook.1. If the curve C is parameterized by ht2− t, 2t + 4i, then compute:(a) ds =(b) d~r =(c) Set up the arc length integral for 0 ≤ t ≤ 1.2. If the surface S is parameterized by hx, y, 3x2− xy + 5i then compute:(a) ~rx× ~ry=(b) d~S = dS =(c) Set up the integral for the surface area over the rectangle 0 ≤ x ≤ 3, −1 ≤ y ≤ 2(d) The surface normal, ~n =(e) If the vector field~F = hx, y, z2i, set up the integral:RRS~F · d~S13. IsZC~F · d~r =ZCf(x, y) ds? Explain.4. IsZZDg(x, y, z) dS =ZZS~F · d~S? Explain.5. IsRC~F · d~r =RCP dx + Q dy?6. IsRRS~F · d~S =RRS~F · ~n dS?7. Given surface S over domain D, isRRS~F · dS =RRD~F · (~rx× ~ry) dA?28. Set up the integral (DO NOT EVALUATE) representing the flux of~F across the surfaceS, if the orientation is upward, and~F = hy, x, z2i z = 4 − x2− y20 ≤ x ≤ 1, 0 ≤ y ≤ 19. Set up the integral for the surface area of 4x − 2y + 2z = 4 above the unit circle in theplane.10. Set up the integralRRSy dS, if the surface is given by the part of the cone x2+ y2= z2that lies between the planes z = 1 and z =