Evaluate the improper integral: $\int _ { 0 } ^ { \infty } x ^ { 5 } e ^ { - x ^ { 5 } / 6 } d x$ Round to two decimal places, if necessary.
A) 1.5
B) 2
C) 1
D) Undefined

Question

Quizplus · Accepted Answer

The integral can be solved using the substitution $ u = x^5/6 $, which transforms the integral into a Gamma function $\Gamma(n)$ with $ n = 1 $, resulting in a value of 1.

Evaluate the Improper Integral ∫0∞x5e−x5/6dx\int _ { 0 } ^ { \infty } x ^ { 5 } e ^ { - x ^ { 5 } / 6 } d x∫0∞​x5e−x5/6dx

Evaluate the Improper Integral $\int _ { 0 } ^ { \infty } x ^ { 5 } e ^ { - x ^ { 5 } / 6 } d x$