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In this section, we will define what it means for an integral to be improper and begin investigating how to determine convergence or divergence of such integrals.
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We might have one (or both) of the limits of integration being infinite.
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The function could have an infinite discontinuity somewhere in the interval [a, b].
![The function could have an infinite discontinuity somewhere in the interval [a, b].](http://images.slideplayer.com./15/4550004/slides/slide_4.jpg "The function could have an infinite discontinuity somewhere in the interval [a, b].")
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We will use limits. If exists, then we say I converges to this value, otherwise it diverges.
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Suppose f has an infinite discontinuity at x = a. If exists, then we say I converges to this value, otherwise it diverges. Suppose f has an infinite discontinuity at x = b. If exists, then we say I converges to this value, otherwise it diverges.
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Determine whether the integral converges or diverges. If it converges, state to what value.
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