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