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Find this improper integral?

Find the improper integral of te^-st dt from 0 to b where the limit of b approaches to positive infinity.

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Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

Use integration in parts

∫0b t e-st dt = -(1/s) t e-st (from o to b) + (1/s)∫0b e -st dt = -(b/s) e -sb - (1/s2) e -sb (from 0 to b) =

                          -(b/s)e - sb - (1/s2) e -sb + 1/s2

Now, if you take limes b →∞ you will get:  ∫ = 1/s (answer)