Consider the following: ∫ x 3 x 1 arctan ⁡ t d t

hornejada1c

hornejada1c

Answered

2022-07-10

Consider the following:
x 3 x 1 arctan t d t

Answer & Explanation

potamanixv

potamanixv

Expert

2022-07-11Added 15 answers

If t > 1, then arctan ( t ) ( π / 4 , π / 2 ) and hence
2 π < 1 arctan ( t ) < 4 π
and
2 2 x π < x 3 x d t arctan ( t ) < 4 2 x π
Thus
lim x x 3 x d t arctan ( t ) = .

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