Consider-the-series-I-n-1-e-x-lnx-n-dx-and-I-0-1-e-xdx-Which-of-the-following-is-true-a-0-I-n-e-2-n-2-b-1-I-n-e-2-n-1-c-I-n-is-negative-

Question Number 113865 by Ar Brandon last updated on 15/Sep/20

Consider the series I_{n} = \int_{1}^{e} x {(lnx)}^{n} dx and I_{0} = \int_{1}^{e} xdx

Which of the following is true ?

a ∖ 0 ⩽ I_{n} ⩽ \frac{e^{2}}{n + 2} b ∖ 1 ⩽ I_{n} ⩽ \frac{e^{2}}{n + 1} c ∖ I_{n} is negative