Evaluate the improper integrals:
(a) ∫ 0 ∞ x e − x d x {\displaystyle \int _{0}^{\infty }xe^{-x}~dx}
(b) ∫ 1 4 d x 4 − x {\displaystyle \int _{1}^{4}{\frac {dx}{\sqrt {4-x}}}}
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