Question

3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x, y)| x2 + y² <1, x +y > 1} (b) sin(x2 + y2)dA, D is in the third quadrant enclosed by D r? + y2 = 7, x² + y2 = 24, y = 1, y = V3r.

Answer 1

x+y da SS. ,D2 f (414): 8² ty? {1, 247 21} x2 + y2 x²73 = 1 rosa trano Some akanda exty=) 12 0 (inutioso) (sinut osa) drad Song ksinet ose) th (sinat osa) ("- shot ose Th --- -coso t sino no 2- 4-1 Ansi = S sin x² + y 2, da / p is in the third quadrant enclosed by - x2 +y = 11 , x² + y2 = 25, y =X, Y = 33*

Y = √3x .Yox Ya- x² + y2 = - du x2 tynn 25 Yax- Yarsu SS Sin (22 + y²) a A D -17 r sin (²) dr do a r= Jr 2 ſmo sinudu da 2T 11 -1/4 517/3 cosul T -1/4 dQ -4. (-3 1 s da -Та --4 "Is incense en in 61² tyg & A = #13