Practice question · Select all that apply
Select every integral that is improper.
Hints
- Improper means an infinite limit or an integrand that blows up somewhere in the interval.
- Check whether 1/x is bounded on each of the two intervals it appears in.
Show the answer
- C. e^(-x) dx from 1 to infinity
- D. e^x dx from minus infinity to 0
- E. 1/x dx from 0 to 1
Why
1/x blows up at the left endpoint 0, so the first is improper; the last is perfectly ordinary because 1/x is bounded on [1,2]. Options 3 and 4 have infinite limits. A bounded integrand on a bounded interval is never improper.
Practise Improper Integrals
The app has 6 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
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