My study manual defines "e-circle sub x" as E(T(X)) and defines that as the integral over the defined interval of the Survival function of T(X) ie integral of t

**p**x. This varies from the usual expected value equation which is the integral of t times f(t) dt. I notice that it can be evaluated both ways. That implies that x times "force of mortality" of t+x is 1. Is this true? If so can anyone explain why it is true?
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