There are two types of improper integrals:
1) Type 1
a) ∫a∞f(x)dx=limt →∞∫atf(x)dx
b) ∫−∞bf(x)dx=limt →−∞∫tbf(x)dx
2) Type 2
a) If f is continuous on [a,b) and discontinuous at b, then:
b) If f is continuous on (a,b] and discontinuous at a, then:
c) If f has a discontinuity at c, where a<c<b, then: ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx
If the limits exist and is finite, then it is convergent. Otherwise, it is divergent.
Type 1 integrals with part a
Type 1 integrals with part b
Determining convergence and divergence with type 2 integrals
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