# why is hazard function tending to infinity

How to prove that if h(t) hazard function is failure rate function then integration of h(t) from 0 to infinity is infinity .

The cumulative hazard function $$\Lambda(t) = \int_{0}^t h(s) ds$$ is related to the survival function by $$S(t) = \exp(-\Lambda(t))$$. The survival function is cadlag starting at 1 at time 0 and tending to 0 as $$t \rightarrow \infty$$. Therefore $$\Lambda(t) \rightarrow \infty$$ as $$t \rightarrow \infty$$.