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Question Number 174421 by ali009 last updated on 31/Jul/22

1) s h o w t h a t

\int_{- 1}^{1} \frac{- d x}{\sqrt{x^{2} + 2 x + 2}} = l n (\sqrt{5} - 2)

2)

d e t e r m i n e

\int_{1}^{\infty} \frac{d x}{(x + 1) \sqrt{x}}

3) t e s t t h e c o n v e r g e n c e o f t h e s e r i e s g i v e n b y

\underset{r = 1}{\sum^{\infty}} \frac{(r + 1)!}{r! (e^{r})}

4)

o b t a i n 3 n o n z e r o t e r m s o f m a c l a u r r i n s

s e r i e s f o r {s i n}^{2} (x), h e n c e e v a l u a t e

\int_{0}^{0.5} \frac{{s i n}^{2} (x)}{x^{2}} d x

g i v e n y o u r a n s w e r c o r r e c t t o 4 d e c i m a l

p l a c e s