let f(x) =∫_0 ^(π/2) ln(cosθ +xsinθ)dθ with x fromR 1) determine a explicit form for f(x) 2) calculate ∫_0 ^(π/2) ln(cosθ +sinθ) dθ and ∫


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Question Number 59052 by maxmathsup by imad last updated on 04/May/19

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