Question

please solve it with polor coodinate graph

4. Find the area. a. Inside one leaf of the three-leaved rose cos30 r= b. Shared by the circle r 2 and the cardioid r 2(1+sin 0) c. Inside the circle r-3 cos 0 and outside the cardioid r=1 - cos0 d. Inside the circle r 4 sin0 and below the horizontal line r 3 csc e. Inside the outer loop of the limason r1-2 cos f. Inside the lemniscate 6 sin20 and outside the circle r= V3

Answer 1

a-) r= cos(3e) A = 2 rcos (30) 띠6 (CDS 30do CDS 30de x 2 X 2 14-COS0 S. do 2 Sin6e77 o)-(sinT-ino) 12

r Gsin20 (lemniscate) r (cirle sin (20) ST x는( (in (20))3 de A 2 까고 S2 'LoS J#]12 A = -3 끼12 have Sinlu )d u-3 히2 do So we O- 20 du = 2d0 Consider ST12 A = - 3 COS() 5T A -3 12 12 -( A= 343-ㅠ

Lne (0,2 Arta of shaded regivc Arca of drcle meets rcle at 4sino=3 02 (oY T Sin Area (reqired Area 0f rc -6 (1stno Yao 3 Loseco H (Lo+02-1ot0) 1COS29 Coto Jei. - (-) '() 2 in (245 Sin(202)-Sin20) JAviaeste-) A =

Lne (0,2 Arta of shaded regivc Arca of drcle meets rcle at 4sino=3 02 (oY T Sin Area (reqired Area 0f rc -6 (1stno Yao 3 Loseco H (Lo+02-1ot0) 1COS29 Coto Jei. - (-) '() 2 in (245 Sin(202)-Sin20) JAviaeste-) A =

r- 2(+Cos e) b. 2 2 A = 2 de A = +2cos Cos'e )do A2 J-12 1COS de 2. sin20 8+3T 3M-8 A = A, + A 2 = 2T+3T-8 = 5w&

r- 2(+Cos e) b. 2 2 A = 2 de A = +2cos Cos'e )do A2 J-12 1COS de 2. sin20 8+3T 3M-8 A = A, + A 2 = 2T+3T-8 = 5w&

) -20se) maior 31T scos) using ymmhyds twice area A 2 OP (asont -) 372 +coS29 37 32 COS20 (0)4 2 3可 Sin20 2 Sin(3) 3 3TT + 2. 2.