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It Can Be Shown That $\int _ { 0 } ^ { \infty } x e ^ { - x } d x$

Question 19

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It can be shown that $\int _ { 0 } ^ { \infty } x e ^ { - x } d x$ = 1. Use this fact and the integral test to construct an appropriate convergent infinite series. Is $\sum _ { \mathrm { k } = 0 } ^ { \infty } \mathrm { e } ^ { - \mathrm { k } }$ the correct series?

It Can Be Shown That ∫0∞xe−xdx\int _ { 0 } ^ { \infty } x e ^ { - x } d x∫0∞​xe−xdx

True/False

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It Can Be Shown That $\int _ { 0 } ^ { \infty } x e ^ { - x } d x$

Correct Answer:
Verified
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