Question

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

Answer 1

Answer:convergent

Step-by-step explanation:

Given

Improper Integral I is given as

$I=\int_{-\infty}^{0}1000e^xdx$

$I=1000=\int_{-\infty}^{0}e^xdx$

integration of $e^x$ is $e^x$

$I=1000\times \left [ e^x\right ]^{0}_{-\infty}$

$I=1000\times I=\left [ e^0-e^{-\infty}\right ]$

$I=1000\times \left [ e^0-\frac{1}{e^{\infty}}\right ]$

$I=1000\times 1=1000$

so the integration converges to 1000 units