Definition of Improper Integrals

Improper integrals are used to calculate the solutions to definite integrals that may not necessarily exist because the functions are either discontinuous or have indefinite limits. The solution to an improper integral can be calculated as a limit, as long as the limit exists and can be calculated. In this case, the improper interval is convergent. If the limit doesn't exist, or if it converges to ±∞, then the improper integral is divergent. For a function f(x) over the interval [a, ∞], . For the function f(x) over the interval [−∞, b], . In general, to solve an improper integral, replace the ±∞, limit with a variable (t), and then take the limit of the integral as t approaches ±∞

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