(x)h==l((当x=a时=a,当x=b时 例1计算√a2-x2dx(a>0) 解 xdx 今x= aint2 acost acos stdt 2兀 2 2 cos tdt=2(+cos2)dt It+sin 2t12=no Vat-x2=vat-ausinit=acost, dx=acostdt 当x=0时t=0,当x=a时t=x. 首页上页返回结束铃首页 上页 返回 下页 结束 铃   −  = 2 0 sin 0 2 2 cos cos  a x dx a t a tdt 解 a 令x a t 例 1 计算 − a a x dx 0 2 2 例1 (a>0) 提示： a x a a sin t acost 2 2 2 2 2 a − x = a −a sin t =acost , dx=acostdt  2 2 2 2 2 − = − = , dx=acostdt    = = 2 + 0 2 2 0 2 2 (1 cos2 ) 2 cos   t dt a a tdt 2 2 0 2 4 1 sin 2 ] 2 1 [ 2 t t a a   = + =    = = 2 + 0 2 2 0 2 2 (1 cos2 ) 2 cos   t dt a a tdt 2 2 0 2 4 1 sin 2 ] 2 1 [ 2 t t a a   = + =  f x dx f t t dt b x t a ( ) [ ( )] ( ) ( )    a     令 = (当 x=a 时 t=a, 当 x=b 时 t=) 下页   −  = 2 0 sin 0 2 2 cos cos  a x dx a t a tdt a 令x a t   −  = 2 0 sin 0 2 2 cos cos  a x dx a t a tdt a 令x a t 当 x=0 时 t=0, 当 x=a 时 2  t= 