संकलनो का मान ज्ञात कीजिएः
`int_(0)^(1) sin^(-1)x dx`

Explanation

यहाँ `I=underset(0)overset(1)int sin^(-1)x dx`
माना `sin^(-1)x=t rArr x=sin t rArr dx =cos tdt`
जब `x=0 rArr t=sin^(-1) 0=0`
और `x=1 rArr t=sin^(-1)1 =(pi)/(2)`
`therefore I=underset(0)overset(pi//2)int underset(I)(t). underset(II)(cos t) dt`
`=[t sin t]_(0)^(pi//2)-underset(0)overset(pi//2)int sin t dt`
`=[t sin t]_(0)^(pi//2)-[-cos t]_(0)^(pi//2)`
`=[pi/2sin""pi/2-0]-[-cos""pi/2+cos0]`
`=pi/2xx1-(0+1)=pi/2-1`