Evaluate the Integral $\int_{0}^{8}\left(x^{2}+8\right) e^{-x} d x$ A) $30 e^{-4}+10$ B) $-30 e^{4}+10$

question 39

Multiple Choice

Evaluate the integral. $\int_{0}^{8}\left(x^{2}+8\right) e^{-x} d x$

• A) \(30 e^{-4}+10\)
• B) \(-30 e^{4}+10\)
• C) \(-90 e^{-8}+10\)
• D) \(-30 e^{-4}-1\)
• E) \(\text { None of these }\)

---

Definitions:

Standard Deviation

A statistic that quantifies the dispersion or variability of a dataset, measuring the average distance between each data point and the mean.

Z-score

A quantitative measure that demonstrates the correlation of a specific value to the mean of a dataset, identifying its separation from the mean by counting the standard deviations.

Standard Normal Random Variable

A type of random variable that has a mean of 0 and a standard deviation of 1, following the standard normal distribution.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values differ from the mean of the data set.