Question

Convergence in mathematics ​

Answer 1

that looks so complicated im dropping out

Explanation:

Answer 2

Converges to
`(√(\pi ))/(2)`

Explanation:

`\int _0^(\infty \:)e^(-x^2)dx` =
`\lim_(b \to \infty)`
`\int _0^(b \:)e^(-x^2)dx` =
`(√(\pi ))/(2)`

steps:

write improper integral as a limit

solve integral

apply limit

If limit exists and this number is finite, the improper integral converges