7.8.pdf - 7.8 Improper Integrals Improper Integrals are said to be \u2022 Convergent if the limit is finite and that limit is a value of the improper

# 7.8.pdf - 7.8 Improper Integrals Improper Integrals are...

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7.8 Improper Integrals Improper Integrals are said to be: Convergent , if the limit is finite and that limit is a value of the improper integral. Divergent , if the limit DNE. Type 1: Infinite Intervals Integrals with infinite limits of integration. 1) If is continuous on , then (provided that thee limit exists as a finite number.) 2) If is continuous on , then (provided that thee limit exists as a finite number.) 3) If is continuous on , then (where c is any real number.) The integral on the left side of the equation is convergent if only if both improper integrals on the right side are convergent. Otherwise, it is divergent and has no value. Type 2: Discontinuous Integrands Integrals of functions that become infinite at a point within the interval of integration. 1) If is continuous on , then (provided that thee limit exists as a finite number.) 2) If is continuous on , then (provided that thee limit exists as a finite number.) 3) If has a discontinuity at , where , and both and are convergent, then