Saved Bookmarks
| 1. |
`int_(1//3)^(3)(1)/(x)log_(e)(|(x+x^(2)-1)/(x-x^(2)+1)|)dx` is equal toA. `(8)/(3)`B. `-(8)/(3)`C. 0D. 3 |
|
Answer» Correct Answer - C `I=int_(1//3)^(2)(1)/(x)log_(e)(|(x+x^(2)-1)/(x-x^(2)+1)|)dx` Let `x=(1)/(t)rArr dx =-(1)/(t^(2))dt` `rArr" "I=-int_(3)^(1//3)tlog_(e)(|((1)/(t)+(1)/(t^(2))-1)/((1)/(t)-(1)/(t^(2))+1)|)(1)/(t^(2))dt` `" "=int_(1//3)^(3)(1)/(t)log_(e)(|(t-t^(2)+1)/(t+t^(2)-1)|)dt` `" "=-int_(1//3)^(3)(1)/(x)log_(2)(|(x+x^(2)-1)/(x-x^(2)+1)|)dx` `rArr" "I=-IrArr I=0` |
|