InterviewSolution
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InterviewSolution
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इन संकलनो का मान ज्ञात कीजिएः `int_(0)^(2) xsqrt(x+2)dx` |
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Answer» यहाँ `underset(0)overset(2)int xsqrt(x+2)dx` माना `x+2=t rArr x=t -2 rArr dx=dt` जब `x=0 rArr t=0+2=2` और `x=2 rArr t=2+2=4` `therefore I=underset(2)overset(4)int (t-2)sqrtt dt` `rArr I=underset(2)overset(4)int (t^(3//2)-2t^(1//2))dt` `rArr I=[2/5t^(5//2)-2xx2/3t^(3//2)]_2^(4)` `rArr I=[2/5t^(2)xx(4)^(5//2)-(4)/(3)xx(4)^(3//2)]-[2/5xx(2)^(5//2)-4/3(2)^(3//2)]` `rArr I= [2/5xx32-4/3xx8]-[2/5xx4sqrt2-4/3xx2sqrt2]` `rArr I=2/5[32-4sqrt2]-4/3[8-2sqrt2]` `rArr I=(64)/(5)-(8sqrt2)/(5)-(32)/(3)+(8sqrt2)/(3)` `rArr I=((192-160)/(15))+8sqrt2 ((5-3)/(15))` `rArr I=32/15 +(16sqrt2)/(15)=(16sqrt2)/(15)(sqrt2+1)` |
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