Elementary differential equations and boundary value problems

4. Prove the following: F(s) A} If [f(t)} = 13(3),. then 1; {[5 f(x)dx} = _ .5' B) Use A) to nd L{Si(t)} = L {Itsmm dx} 0 x T St C) Prove, if f{t) has period T > 0, {f(t)} = % D) Use part C) to nd {f(t)}, where f (t) = t2 on [-n, It], t + 2n) =f{t)