Question

Change the order of integration. 6" | vx2 + 16 dx dy The answer should be in the form See f(x, y) dy dx, where a sx sb and g1(x) < y = 82(x) are the bounds of the integration region. (Use symbolic notation and fractions where needed.) a= b= 81(x) = 82(x) =

Answer 1

ordu a) changing sation + Jo si ſxe 16 de of Intary de dy Antwer and be in form 1 pon p614) dy dx g, (n) gi (G) Sy Ega (A) From Integral weget arry, gn, neh. where a bacb + n = 4 y = 0, y = 16 1 out. Yz16 92 x (0/0 you 711 - yu. Tyala- o to x By changing onde g ranges from & ranges from o to 4 we get 1 as , to veget $ 1 b=.4 V + 16 dy de 4 0 1 gG) J₂G) - Voc Evaluation CS Samed.th CamScanner

so (vx x 3416 Tx) dx arxe 16 de 312 du तज 11 Let uz a ૪િ du fr dne 35 rzu² I= 22 Ju²116 du. Performing trigonometric the Substitution weget a=4 ton (V) v = are tan / u du = 4 See 4v) dv. Ja see? (v) r 16 tant with cu see 3D du. Applying Reduction (v) due see Iz 16 formula. (0-2) v ton (u) Jeen video are free 7² (1) out with De 3 I= bee votan ( et af lee u du bec (V) tan (y) en (tas (U)+ tee (V) 2 ise to weget I= 8 ted us der (V) p8er (tas(u+ bec CV) substitution Ve tant / 4 tan (itan f'tes" (#1) 24 indoring *** CS Scanned with CamScanner

.pl I= 8 ln kec (to" (+)) - (Vietti + ) takvo Finally weget 16 In Just at 1+4) + 49 7 3/3 j vuelo du a 32 A el t 40 ec indering substitution uca le I = 16 de lei 24h 3 I = 16 ln (Vx+16 +222 96) le Jast 16 tc Linet eweger substituting 8 I Nara 8 en (tark) I= + 32 √5 2 3 3 31.089078096 116 Somo s 31.058 078096, H x 16 dady 1 x3,16 dy du = 31. &&078096 116 129 116 au dy Juan vg (* Kindly like for Solution) Scanned with CamScanner CS