Improper integral convergence

The Laplace transform of a function//) is defined by F(s) = L f(t) = I(Te s/(f) dt, where s is a complex variable. Note that the transform is an improper integral and therefore may not exist for all continuous functions and all values of s. We restrict consideration to those values of s and those functions/for which this improper integral converges. The Laplace transform is used in process control (see Sec. 8). 

If the limit exists, then the improper integral converges otherwise, the improper integral diverges. Given/(x) on [a,b] such that/(a) = then the improper integral is defined as... 

EXAMPLE 5.9 Determine whether the following improper integral converges, and if so, find its value ... 

Determine whether the following improper integrals converge. Evaluate the convergent integrals. 

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