- #1

- 775

- 1

If one of the integrals on the right-hand-side is known to diverge, must the integral on the left also necessarily diverge?

BiP

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- Thread starter Bipolarity
- Start date

- #1

- 775

- 1

If one of the integrals on the right-hand-side is known to diverge, must the integral on the left also necessarily diverge?

BiP

- #2

- 22,089

- 3,296

Yes, by definition of improper integrals.

- #3

- 210

- 10

[tex] \int_{1}^{2} \frac{1}{x}dx [/tex] converges, but [tex] \int_{1}^{-1}\frac{1}{x}dx + \int_{-1}^{2} \frac{1}{x}dx [/tex] diverges (each term is an integral over a region containing 0, where 1/x is unbounded).

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