2.12.29 Asymptotic Analysis

Condition: prove the asymptotic formula: \ [\ begin {array} {l} \ int_ {0}^{a} t^{\ alpha-1} e^{-\ lambda t} d t \ sim \ gamma (\ alpha) \ lambda^{-\ alpha} \\ \ lambda \ rightarrow+\ infty, \ quad a> 0, \ quad \ alpha> 0. \ end {Array} \]