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WZ
Numerade Educator

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Problem 61 Hard Difficulty

(a) Show that $ \displaystyle \int_{-\infty}^\infty x\ dx $ is divergent.
(b) Show that
$$ \lim_{t\to\infty} \int_{-t}^t x\ dx = 0 $$
This shows that we can't define
$$ \int_{-\infty}^\infty f(x)\ dx = \lim_{t\to\infty} \int_{-t}^t f(x)\ dx $$

Answer

a. $I$ is divergent.
b. $\int_{-\infty}^{\infty} x d x \neq \lim _{t \rightarrow \infty} \int_{-t}^{t} x d x$

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Video Transcript

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