13.函数f (x) =〈|(x sin , x 士 0 在x = 0 处间断,则该点为( D )。 |l 1 , x = 0

13.求定积分j02x - 1dx
解:
= j01 x - 1dx + j12 x - 1dx
= j01 (1- x)dx + j12 (x - 1)dx
= 1- + x2 null - 1
= 1

12.求定积分j-12 .
解:
= j-12 . d (11+ 5x)
= - [(11+ 5x)-2 ]1-2
= - (16-2 - 1) 51
= 512

2

11.求定积分j nullxedx 。
解:
= (ej)01 xdx = e . x2 null
e
=

10.求j-01 dx
解: j-01 dx = j-01 3x2 + ))|dx
= [x3 ]0-1 + [arctan x]0-1
=1+

9.计算j-+w 的值.
解: j-+w = [arctan x]null
=

8.计算j01 e dx .
解:先用换元法:令 = t ,则 x = t2 ,dx = 2tdt ,且
当x = 0 时, t = 0 ;当 x = 1 时, t = 1 .
换元后分部积分, j01 e dx = 2j01 tet dt = 2j01 td(et )= 2([tet ]null - j01 et dt)
= 2(e - [et ] )null = 2[e - (e - 1)]= 2

3 6

7.求定积分j12 (1 + )dx .
解: j12 (1 + )dx = j12 ( + x)dx
「 ( 3 ) ]2
= | + |
= +

1
= 3