Decide Whether the Integral Converges $\int _ { - 2 } ^ { + \infty } e ^ { - 0.5 x } \mathrm {~d} x$

question 42

Essay

Decide whether the integral converges. If the integral converges, compute its value.
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If the integral diverges, enter your answer as diverges .
​ $\int _ { - 2 } ^ { + \infty } e ^ { - 0.5 x } \mathrm {~d} x$

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Definitions:

Altar of Zeus

A monumental construction built in Pergamon (now Turkey), celebrated for its rich sculptural frieze depicting the Gigantomachy, the battle between gods and giants in Greek mythology.

Pergamenes

Refers to the people from ancient Pergamon, a rich and powerful ancient Greek city located in the modern-day territory of Turkey.

Drapery

Cloth artistically arranged and depicted in art to cover, protect, or adorn figures or objects, highlighting texture and movement.

Parthenon East Pediment

The sculptural group located at the eastern end of the Parthenon in Athens, depicting the birth of Athena from the head of Zeus.