संकलनो का मान ज्ञात कीजिएः
`int_(0)^(pi//2) sqrt(sin phi) cos^(5) phi dphi`

Explanation

यहाँ `underset(0)overset(pi//2)int sqrt(sin phi) cos^(5) phi dphi`
`rArr I=underset(0)overset(pi//2)int sqrt(sinphi).cos^(4) phi. cos phi d phi`
`rArr I=underset(0)overset(pi//2)int sqrt(sinphi)(1-sin^(2) phi)^(2)cos phi d phi`
माना `sin phi=t rArr cos phi=dt `
जब `phi=0rArr t=sin 0=0`
और `phi=pi/2 rArr t=sin "pi/2=1`
`therefore I=underset(0)overset(1)int sqrtt (1-t)^(2)dt`
`=underset(0)overset(1)int sqrtt(1-2t^(2)+t^(4))dt`
`=underset(0)overset(1)int (sqrtt-2t^(5//2)+t^(9//2))dt`
`=underset(0)overset(1)int (t^(1//2)-2t^(5//2)+9^(//2))dt`
`=[2/3t^(3//2)-2. 2/7t^(7//2)+2/11t^(11//2)]_(0)^(1)`
`=(2/3-4/7+2/11)-0=64/231`