1) let f(x) =∫_0 ^(2π) ((cost)/(3 +sin(xt)))dt find a explicit form of f(x) 2) calculate g(x) =∫_0 ^(2π) ((tcos(xt)cost)/((3 +sin(xt))^2 ))dt 3) calculate ∫_0 ^(2π) ((cost)/(3+sint)) and ∫


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Question Number 55271 by maxmathsup by imad last updated on 20/Feb/19

$1) l e t f (x) = \int_{0}^{2 π} \frac{c o s t}{3 + s i n (x t)} d t$ $f i n d a e x p l i c i t f o r m o f f (x)$ $2) c a l c u l a t e g (x) = \int_{0}^{2 π} \frac{t c o s (x t) c o s t}{{(3 + s i n (x t))}^{2}} d t$ $3) c a l c u l a t e \int_{0}^{2 π} \frac{c o s t}{3 + s i n t} a n d \int_{0}^{2 π} \frac{t {c o s}^{2} t}{{(3 + s i n t)}^{2}} d t$
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