Calculus › Section I · Integration techniques and improper integrals › Topic I.8
Improper integrals
Some regions stretch to infinity or hide a vertical asymptote inside them. Improper integrals extend the definite integral to these cases, and the surprising news is that an infinitely long region can still have finite area.
In this topic
- When infinity sneaks in
- Infinite intervals are limits
- Worked example: a convergent tail and a divergent one
- The p-integral benchmark
- Blow-ups at a point: the second kind
- Asymptotes hiding inside
- Exponential tails
- Worked example: what is a perpetuity worth?
- The comparison test for integrals
- Common mistakes to avoid
- Key takeaways
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Standards: 6 (BC)