The definite integral is defined as the limit of a sum under two conditions (i) the interval [*a*, *b*] is of finite length and (ii) *f* is defined and bounded on [*a*, *b*]. Then is called a **proper integral.**

But there are many practical problems where *f* is unbounded on [*a*, *b*] or the interval is not finite. Such integrals are known as **improper integrals**.

For example: are improper integrals.

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