Evaluate the improper integral $\int _ { 0 } ^ { \infty } x e ^ { - x / 2 } d x$
A)1
B)2
C)4
D) $\frac { 1 } { 4 }$
E) $\frac { 1 } { 3 }$
F)3
G) $\frac { 1 } { 2 }$
H)Divergent

Name: Evaluate the improper integral $\int _ { 0 } ^ { \infty } x e ^ { - x / 2 } d x$ A)1 B)2 C)4 D) $\frac { 1 } { 4 }$ E) $\frac { 1 } { 3 }$ F)3 G) $\frac { 1 } { 2 }$ H)Divergent
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Question

Evaluate the improper integral $\int _ { 0 } ^ { \infty } x e ^ { - x / 2 } d x$ 
A)1
B)2
C)4
D) $\frac { 1 } { 4 }$ 
E) $\frac { 1 } { 3 }$ 
F)3
G) $\frac { 1 } { 2 }$ 
H)Divergent

Quizplus · Accepted Answer

The integral can be solved using integration by parts or recognizing it as a gamma function. The result is 4.

Evaluate the Improper Integral ∫0∞xe−x/2dx\int _ { 0 } ^ { \infty } x e ^ { - x / 2 } d x∫0∞​xe−x/2dx

Evaluate the Improper Integral $\int _ { 0 } ^ { \infty } x e ^ { - x / 2 } d x$