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Question Number 47060 by maxmathsup by imad last updated on 04/Nov/18

l e t f (x) = \int_{0}^{1} \frac{d t}{2 + c h (x t)}

1) f i n d a e x p l i c i t f o r m o f f (x)

2) c a l c u l a t e g (x) = \int_{0}^{1} \frac{t s h (x t)}{{(2 + c h (x t))}^{2}} d t

3) f i n d t h e v a l u e o f \int_{0}^{1} \frac{d t}{2 + c h (3 t)} a n d \int_{0}^{1} \frac{t s h (3 t)}{{(2 + c h (3 t))}^{2}} d t

4) c a l c u l a t e u_{n} = \int_{0}^{1} \frac{d t}{2 + c h (n t)} w i t h n n a t u r a l i n t e g r a n d s t u d y t h e c o n v e r g e n c e

o f t h e s e r i e Σ \frac{u_{n}}{n} .