Integration -3

Calculus Level 5

If \(\displaystyle I_n = \int_0^1 \dfrac{(\ln x)^n }{\sqrt x} \, dx \), then of which of the following is/are true?

Choose the most precise option.

(A): \(I_n\) has a finite value for all positive integers \(n\).
(B): \(\dfrac{I_2}{I_1} + \dfrac{I_3}{I_2} + \dfrac{I_4}{I_3} = -4\).
(C): \(I_4 = -9\).
(D): \(I_8 = 40331\).

×

Problem Loading...

Note Loading...

Set Loading...