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