let I(x)= ∫_0 ^π (dt/(x^2 +cos^2 t)) 1) prove that I(x)= 2∫_0 ^(π/2) (dt/(x^2 +cos^2 t)) 2) find the value of I(x).


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Question Number 30216 by abdo imad last updated on 18/Feb/18

$l e t I (x) = \int_{0}^{π} \frac{d t}{x^{2} + {c o s}^{2} t}$ $1) p r o v e t h a t I (x) = 2 \int_{0}^{\frac{π}{2}} \frac{d t}{x^{2} + {c o s}^{2} t}$ $2) f i n d t h e v a l u e o f I (x) .$
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