Question

ework assignments. Please see the course syllabus for This one is due at the beginning 1. (5 pts.) TRUE OR FALSE: (a) Let R denote a plane region, and (u,v) (u(,y),v)) be a different set of coordinates for the Cartesian plane. Then for any function F(u,v) F(u, v)dudvF(u(r, y),v(x, y))dzdy (b) Let R denote a plane region, and (u, v) (u(r, w),v(x, y)) be a different set of coordinates for the Cartsian plane. Then do (c) Let R denote a square of sidelength 2 defined by the inequalities |rl 1, lyl s 1, and (u, u)-(3y, 2r). Then the area of R is computed as dudv. (d) Let R denote a square of sidelength 2 defined by the inequalities Irl S 1, yl s 1, and (u, v) (3y,2x). Then the area of R is computed as (1/6)dudv. (e) Let R denote a square of sidelength 2 defined by the inequalities rls1, lul s1, and (u, u)-(3y, 22). Then the area of R is computed as (1/6)dude. 2. (3 pts.) Using cylindrical coordinates, set up the integral to find the volume of the region enclosed by the vertical cylinder +y4 and the planes0 and y+z 4 PrtScn Home End F4 FS F6 F7 F8

Answer 1

Solot on step gu) here, y) at u,v) (al Given tadu meh

and din, y) duo, v) dlo dv -3 2 4