Determine whether the improper integral converges or diverges, and find the value of each that converges.

Mathematics

1 answer:

yuradex [85]2 years ago

6 0

Answer:

Converges to 0

Step-by-step explanation:

Given is an improper integral where a= -infinity, b = infinity and

f $f(x) = \frac{x}{x^2+1}$

$\int\limits^a_b {f(x)} \, dx$

This resembles the above integral where a = -b

f(x) let us check whether odd or even or neither

$f(-x) = \frac{-x}{x^2+1}$ =-f(x)

Since f(x) is odd function and integral is of the form -a to a by properties of integrals, this value is 0

Hence answer is 0

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