5.函数y = 的定义域是( 2 < x < 2 )。

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

6. 求定积分j1+的 的值. 解: j1+的 = 的

10
= 3

5.求定积分j12 (x2 + 1)dx
解: j12 (x2 + 1)dx = + x null
(8 ) ( 1)

4.求定积分j02 cos 2xdx
解:原式= j02 cos 2xd 2x
= [sin 2x]
=0

3.求定积分j04 cos2 xdx
解:原式= j04dx
= j04 dx + j04 dx
= +

2.求定积分j14 dx
解:令 = t ,则 x = t2 ,dx = 2tdt .x = 1 不 t = 1, x = 4 不 t = 2
原式=2j12 dt -( 2)j12 dt =2 - 2[ln(1 + t)]null =2 + 2 ln