⑩天掌 Teaching Plan on Advanced Mathematics 例5求心形线r=a(1+c0所围平面图形的面积 (a>0) 解dA=a(1+c0s0)d6 r=a(1+c0s6) 利用对称性知 6 A=2·a2(1+cosb)2db 0 =a2(1+2c0s0+cos20)d0 a =0+2sin 0+-sin 20 T 2 「返回 Tianjin Polytechnic Moiwendity wTianjin Polytechnic University Teaching Plan on Advanced Mathematics 例 5 求心形线r = a(1+ cos )所围平面图形的面积 (a  0). 解 a (1 cos ) d 2 1 dA 2 2 = + 利用对称性知 d . 2 3 2 = a  d 2 (1+ cos )   =  0 2 2 1 A 2 a (1 2cos cos  )d 2  + +  = 0 2 a       =  +  + sin 2 4 1 2sin 2 2 3 a  0 返回  r = a(1+ cos ) 2a