3.求9dz 解：x=0是产的瑕点，由瑕积分收敛的定义 [女学广a票中r 4.计算∫∫x2 drdy,.其中D是由直线x=0,y=1及x=V万所围成区域. iv- -fia-i(pu-t'ru) -(-+0-×-品 数学分析（山试题第4页（共8页）3. ¦ R 0 −1 1 √3 x dx. ): x = 0 ´ 1 √3 x ×:, d×È©Âñ½Â Z 0 −1 1 √3 x dx = lim η→0+ Z 0−η −1 x − 1 3 dx = lim η→0+ 1 − 1 3 + 1 x − 1 3 +1    −η −1 = 3 2 lim η→0+ x 2 3    −η −1 = 3 2 lim η→0+ [(−η) 2 3 − (−1) 2 3 ] = − 3 2 . 4. OŽ RR D x 2 y dxdy, Ù¥ D ´d†‚ x = 0, y = 1 9 x = √y ¤Œ¤«. )µ D ´ y = x 2 , y = 1 † y ¶Œ¤«. d­È©OŽ{, ké y È ©, ￾é x È©. ò D ÝK3 x ¶þ, «m [0, 1] , ∀x ∈ [0, 1], y l y = x 2 C  y = 1. ZZ D x 2 y dxdy = Z 1 0 dx Z 1 x2 x 2 ydy = Z 1 0 x 2 1 2 y 2    y=1 y=x2 dx = Z 1 0 1 2 x 2 (1 − x 4 )dx = 1 2 Z 1 0 x 2 dx − Z 1 0 x 6 dx = 1 2  1 3 x 3    1 0 − 1 7 x 7    1 0  = 1 2 × 4 21 = 2 21 . êÆ©Û(III)ÁK 1 4 £
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