let f(x) = ∫_0 ^∞ ((x sinx)/(a^2 +x^4 ))dx with a>0
1) find a explicit form of f(a)
2) find g(a) = ∫_0 ^∞ ((xsinx)/((a^2 +x^4 )^2 ))dx
3)find the value of ∫_0 ^∞ ((x sinx)/(x^4 +1))dx
4) find the value of ∫_0 ^∞ ((xsinx)/((x^4 +1)^2 ))dx .
If is an even function defined on
the interval (−5,5) then a value
of x satisfying the equation
f(x)=f(((x+1)/(x+2))) is
a)((−1+(√5))/2) b)((−3+(√5))/2) c)((−1−(√5))/2)
d)((−3−(√5))/2_ )