InterviewSolution
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InterviewSolution
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`int(x^(49)tan^(-1)(x^(50)))/((1+x^(100)))dx=k[tan^(-1)(x^(50))]^(2)+C,` , then k is equal toA. `(1)/(50)`B. `-(1)/(50)`C. `(1)/(100)`D. `-(1)/(100)` |
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Answer» Correct Answer - C Let `l=intx^(49)(tan^(-1)(x^(50)))/(1+(x^(50))^(2))dx` Put`" "x^(50)=t" "rArr" "50x^(49)dx=dt` `therefore" "l=(1)/(50)int(tan^(-1)t)/(1+t^(2))dt` Again, put `tan^(-1)t=u rArr (1)/(1+t^(2))dt=du` `therefore" "l=(1)/(50)int u du =(u^(2))/(100)+C=((tan^(-1)x^(50)))/(100)+C` `"But "l=k(tan^(-1)x^(50))^(2)+C" [given]"` `therefore" "k=(1)/(100)` |
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