Question

1. An iterated double integral that is equivalent to *** dx + ry dy JOR 3. Use Groen's Theorem to set up an iterated double integral equal to the line integral $+eva) dx +(2+ + cow y) dy where is the boundary of the region enclosed by the parabolas y rand 1 = y2 with positive orientation. This yields: A. where R is the triangular region with vertices (0,0),(1,0) and (0,1) is: A B. B. So ['(2-z) dr de SL * 5-0) dy de So L ) dr dy 1 0-0) IL (v=-2gxing") dy de IN"(-1) de dy . C. 2 de dy D D. (3-0) dy dr dy dr (2) (3) f(V1++20%) do + 3ey duy 14. An iterated double integral, in polar coordinates, that is equivalent to the line integral 2. Use Green's Theorem to evaluate 1-2) dr + (x* +yº) dy where R is the region contained between the circles r2 + y2 = 4 and + y2 = 9 in the first quadrant is: A. where C is the closed triangular path from (0,0) to (1.3) to (1.0) to (0,0). This 3r3 cos 20 dr do SL OB. yields: $* / *3r? (cox 20 – win 20) r dr do B.0 6* 3r(cose - sino) r dr do C. $* L *3-* dr do (2) c. D. se (3)

Answer 1

soin 0 Ginen Id(24 de + nydy ) R is shown below. OR Maat Andy we get N - sy compare this with M=89, ам ау Gren's theorem ,ه) 20 ਹੈ 2X -0 styl ارحمه y-ovo x SS (EN OM dy du (y-ody dn. By strip linofy: o→ By region: ein of t:o~ * (y-o) dy du & option (B) is I correct. be + 2y2 dx + 3xydy ny of yox (1,3) By slegion (2) unen, (5+23 Cus shown below. AMR, by strip, ein lum. 20 + of By integral, ME 3 14 1 % +24² Чу , ON By ay & by wreen's theorum we get N=Bry ta x OM 0,03 yo los on 3x dyeln (34-4y) dyan an 0 oy 3x da 0 9 x ² du 2 -4) option (A) is correct H D - 3 2

Gwen Is $(y + er du +(22+ a + Cory? dy below y.zu? Xzył of x toy ¿ is shown By strip lim. : 0² su ofy by region lim. using green 's theorem N = 2x + cosy ² t - Эм 2 ) ay f T3 (2-1) dydx an 2 2 an W Ik dyan option () is correct shown below ♡ Grillen 136 (42-43) dut (3 + y²) dy OR R is using Green's theorem M2 x3 N= x² + y² ON X 3y² ay 3*²-3y 2 dudy In polar, u = 4 Loso, y = dady rardo and ! 2 3 y ӘМ 2 3x12 an I = rsimo and 0:0 I 2 rraro - 123in20) uderdo 3 Jazy 2. 7/2 313 (comodroo 2 so option (AS is correct.