let f(a) =∫_0 ^∞ (dx/(x^n +a^n )) with n integr ≥2 and a>0
1) calculate f(a) intems of a
2) let g(a) =∫_0 ^∞ (dx/((x^n +a^n )^2 )) calculate g(a) interms of a
3) find the values of integrals ∫_0 ^∞ (dx/(x^8 +16)) and ∫_0 ^∞ (dx/((x^8 +16)^2 ))
A boat travels 30km upstream and
44km downstream in 10 hours.
in 13 hours it can travel 40km upstream
and 55km downstream. Determine the
speed of the stream and that of the
boat in still water. (in km/hr)
let f(x) =∫_0 ^∞ ((cos(xt))/(x^2 +t^2 )) dt with x>0
1) find f(x)
2) find the values of ∫_0 ^∞ ((cos(t))/(1+t^2 ))dt and ∫_0 ^∞ ((cos(2t))/(4+t^2 ))dt
3) let U_n =∫_0 ^∞ ((cos(nt))/(n^2 +t^2 ))dt find lim_(n→+∞) U_n and study the convergenge of
Σ U_n and Σ U_n ^2