0-f-r-dr-1-0-g-r-dr-1-i-i-F-t-G-t-dt-F-t-0-f-r-e-rt-dr-G-t-0-g-r-e-rt-dr-

Question Number 222356 by wewji12 last updated on 23/Jun/25

∫_0 ^( ∞) f(r)dr=1 , ∫_0 ^( ∞) g(r)dr=1 ∫_(−∞i+𝛄) ^( ∞i+𝛄) F(t)G(t)dt=?? F(t)=∫_0 ^( ∞) f(r)e^(−rt) dr , G(t)=∫_0 ^( ∞) g(r)e^(−rt) dr

$$\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({r}\right)\mathrm{d}{r}=\mathrm{1}\:,\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{g}\left({r}\right)\mathrm{d}{r}=\mathrm{1} \\ $$$$\int_{−\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} ^{\:\:\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} \:{F}\left({t}\right){G}\left({t}\right)\mathrm{d}{t}=?? \\ $$$${F}\left({t}\right)=\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({r}\right){e}^{−{rt}} \mathrm{d}{r}\:,\:{G}\left({t}\right)=\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{g}\left({r}\right){e}^{−{rt}} \mathrm{d}{r} \\ $$

Answered by MrGaster last updated on 25/Jun/25

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