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Consider the integral `"l"_(1)=int_(1)^(e)(1+x)(x+Inx)^(100)dx. "l"_(2)=int_(sin^(-1)(1//e))^(pi//2) (1 + esinx + Insinx)^(101)cos x dx` If `l_(1)+e/101 l_(2)=(e(1+e)^(101)-k)/101` then `kge` |
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Answer» Correct Answer - A::B::D `I_(1)=int_(1)^(e)x ((1+x)/x)(x+In x)^(100) dx` `=(e(e+1)^(101)-1)/101-1/101 int_(1)^(e)(x+In)^(101)dx` `I_(2)=1/e int_(1)^(e)(t+Int)dt` on taking `e sin x=t` `implies I_(1)+(eI_(2))/101=(e(e+1)^(101)-1)/101impliesK=1` |
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