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Fynjy0 [20]
3 years ago
7

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

Mathematics
1 answer:
Vanyuwa [196]3 years ago
8 0

Answer:

The integral diverges

Step-by-step explanation:

Consider the integral from 0 to infinity of

xe^{4x}

We can do this in parts

\int {xe^{4x} } \, dx =\int {x} \, d(e^{4x})/4\\ = x/4 e^{4x}-e^{4x}/16

When we substitute limits infinity we find that the values become infinity

Hence the integral diverges

The given improper integral diverges

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Answer:

<em>k = - 7.5 </em>

Step-by-step explanation:

Slope "m" of a line through points

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~~~~~~~~~~~~~~~

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2(k - 3) = - 21

k - 3 = - 10.5

<em>k = - 7.5</em>

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