Question

could u help me? thanks

2. First, sketch the region of integration, in the re-plane (meaning: find the boundaries in terms of r and ), of the following integrals, then pass to polar coordinates and compute each of them: (a) [L** dady; (b) »L.6** 2+y’dydr.

Answer 1

Sol 2 (a Na-y² a dx dy y Region of integration : 2 part of cixle x² + y² = 4 x=54-yz 2 Region of integration У ил т-e plans 8=2,0 = 1/2 x=rcoso → 2 8=2 y = y sino dx dy = ydr do Hence, here r varies from a o to 2 & o varies from o to I F/2. ss x dady = (coso) (ordrdo). 2 I Joen 70 D=0 2 g² coso drdo. 0-0 Ar li 83 Y eso de 12 / 3 / (2²-0") caso do 00 11

il wloo coso) do who sino ) ** i sinch) - sem co] - 8 3 = 3 Ang sport x²+ y² dy da Region of integration - y y=&1-22 upper half past ¿ of circle x²=4²=1 8=1 x=0 8=1 G=T Hence, g varies from o to 1 and o varies from o to π co-ordinates (8,0) x+y=r & dydx = 8drdo and , in polar 2 TT 1 I fazyn ditya dy dx g2 (x drdo) 0=0 Y=0

T - 1 1 - le Ś $(14.09) do 89 1 do 0-0 " Oco [ IT do = - -V rola rola 10). (T-0) - 4 vix ss at yh dyda dyda = 1 T S -1 Aug