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If `underset(0)overset(oo)(f)(dx)/((x+sqrt(1+x^(2)))^(5))=(m)/(n)` where m and relatively prime prime, then the value of (m+n) isA. 31B. 30C. 29D. 28 |
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Answer» Correct Answer - A Let `x+sqrt(1+x^(2))=t` `+x^(2)=t^(2)+x^(2)-2txrArr1=t^(2)-2txrArrx=(1)/(2)(t-(1)/(t))rArrdx=(1)/(2)(1+(1)/(t^(2)))dt` Now, `overset(oo)underset(1)(f)(1)/(t^(5))(1)/(2)(1+(t)/(t^(2)))dt=(1)/(2)overset(oo)underset(1)(f)((1)/(t^(5))+(1)/(t^(4)))dt` `I=(-1)/(2)((1)/(4t^(4))+(1)/(6t^(6)))underset(1)overset(oo)| ` `I=(5)/(24)=(m)/(n)` (given) So, (m+n)=29. |
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