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Question Number 28610 by abdo imad last updated on 27/Jan/18

l e t g i v e I (x) = \int_{0}^{\frac{π}{2}} \frac{d t}{\sqrt{{s i n}^{2} t + x^{2} {c o s}^{2} t}} a n d

J (x) = \int_{0}^{\frac{π}{2}} \frac{c o s t}{\sqrt{{s i n}^{2} t + x^{2} {c o s}^{2} t}} d t c s l c u l a t e {l i m}_{x \to 0^{+}} (I (x) - J (x))

a n d p r o v e t h a t I (x) =_{x \to 0^{+}} - l n x + 2 l n 2 + o (1) .