let give a>0
1) find the value of F(a) = ∫_0 ^∞ ((lnt)/(t^2 +a^2 ))dt
2) find the value of G(a)=∫_0 ^∞ ((aln(t))/((t^2 +a^2 )^2 ))dt
3) find the value of ∫_0 ^∞ ((ln(t))/((t^2 +3)^2 ))dt
find the equation of the 2D
curve such that the lines
(x/t) + (y/((a−t) )) = 1
are always tangent to
the curve.
given ′a′ is a positive real
constant and ′t′ is a
parameter. ( 0 < t < a )