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find-0-e-px-dx-0-a-cos-xt-a-2-t-2-dt-with-a-gt-0-p-gt-0-




Question Number 31080 by abdo imad last updated on 02/Mar/18
find ∫_0 ^∞  e^(−px) dx ∫_0 ^a   ((cos(xt))/( (√(a^2  −t^2 ))))dt with a>0 ,p>0
$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{px}} {dx}\:\int_{\mathrm{0}} ^{{a}} \:\:\frac{{cos}\left({xt}\right)}{\:\sqrt{{a}^{\mathrm{2}} \:−{t}^{\mathrm{2}} }}{dt}\:{with}\:{a}>\mathrm{0}\:,{p}>\mathrm{0} \\ $$

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