Question: If s > 0, let g(x) := e-sx for x [0, ]. (a) Use Hake's Theorem to show that g L[0, ] and

If s > 0, let g(x) := e-sx for x ∈ [0, ∞].
(a) Use Hake's Theorem to show that g ∈ L[0, ∞] and ∫10 e-sxdx = 1/s.
(b) Use the Fundamental Theorem 10.3.5.

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