Calculate the Following Integral Exactly $\pi$ $\sqrt { 2 }$ , and So On

question 10

Essay

Calculate the following integral exactly.(Your answer should not be a decimal approximating the true answer, but should be exactly equal to the true answer.Your answer may contain e, $\pi$ , $\sqrt { 2 }$ , and so on.) $\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { z } \int _ { 0 } ^ { y } x ^ { 2 } y ^ { 5 } z ^ { 5 } d x d y d z$

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Definitions:

Standard Deviation

Standard Deviation is a statistic that measures the dispersion or variability of a dataset relative to its mean, indicating how spread out the data points are.

Proportion

A part, share, or percentage that represents a fraction of a whole.

Samples

Selected portions or subsets of a population used in statistical analysis as representations of the entire population.

Standard Deviation

A measure of the dispersion or spread of a set of values, indicating how much the values in the set deviate from the mean.