Question

please with graph

(3pts) Use polar coordinates to setup V x2 + y2dA, where D is J J(D) bounded by y= Vx– x2, y = 0 and y = x V3.

Answer 1

Solution : SS Joc2 + y2 dA Now use polar coordinates x=8caso y = 33120 rsino - 0 then cospotring = 8 dA= rdrdo given y = randce - ③ This is equation of a circle Convert it in general form (X-6) 2+ (Y-k) 2=82 where Chik) - centre of circle and 8 radlicy of circle. 2 = x-x? IN T n²+92_x=0 x-x + 4 + 2 = 4 => (3-3+)?+ (9-oj? (5) centre point (h, k) = (jo) Radius 8= = - 3 + 2 = x 8 cost of resina = reaso ? - 8 caso = [8= casol

another given is = d.13 - ③ This is stright line equation dising roso B =) Sin tano B So of this straight line makes an angle I from x-axis. Y=213 .yzo T/3 caso Now Now SS x ²4 y2 d Aossrordo de D solving: [,65° d0 - 13.30 do I guts caso. (1-sud) do] - 15 60,000 - $773 cos 0 sinho do] 3 L

+ [ 13019/ foo sol [ Sin - 13 6050 siniPod 0] Let sinot cosodo=dt It's t? dt put t= sind 3 [+] Ž [simogats - Ś C so SS Supage du