## Does the integral 1 x 2 diverge or converge?

As sequences, they both converge. As series, 1/x diverges because the sum of its terms does not approach a real number, and 1/x^2 converges because the sum of its terms does approach a real number.

## How do you know if an integral diverges?

Convergence and Divergence. If the limit exists and is a finite number, we say the improper integral converges . If the limit is ±∞ or does not exist, we say the improper integral diverges .

**What does it mean when an integral diverges?**

If the limit is finite we say the integral converges, while if the limit is infinite or does not exist, we say the integral diverges. Convergence is good (means we can do the integral); divergence is. bad (means we can’t do the integral).

### Is the integral convergent or divergent?

Vocabulary Language: English ▼ English

Term | Definition |
---|---|

converge | An improper integral is said to converge if the limit of the integral exists. |

diverge | An improper integral is said to diverge when the limit of the integral fails to exist. |

### What is the integral of x 2?

Integration Rules

Common Functions | Function | Integral |
---|---|---|

Variable | ∫x dx | x2/2 + C |

Square | ∫x2 dx | x3/3 + C |

Reciprocal | ∫(1/x) dx | ln|x| + C |

Exponential | ∫ex dx | ex + C |

**Why is the integral of 1 x divergent?**

Integral of 1/x is log(x), and when you put in the limits from 1 to infinity, you get log(infinity) – log(1)= infinity -0 = infinity, hence it diverges and gives no particular value.

#### How do you know if converges or diverges?

convergeIf a series has a limit, and the limit exists, the series converges. divergentIf a series does not have a limit, or the limit is infinity, then the series is divergent. divergesIf a series does not have a limit, or the limit is infinity, then the series diverges.