Use the Midpoint Rule With $n = 4$ To Estimate the Volume Obtained by Rotating About the Region

question 73

Multiple Choice

Use the Midpoint Rule with $n = 4$ to estimate the volume obtained by rotating about the region under the $y$ -axis the region under the curve.
$$y = \tan x , \quad 0 \leq x \leq \frac { \pi } { 4 }$$
The choices are rounded to the nearest hundredth.

• A) \(V = 0.156\)
• B) \(V = 0.491\)
• C) \(V = 1.851\)
• D) \(V = 0.825\)
• E) \(V = 1.142\)

---

Definitions:

Within-Treatments

Refers to the variability observed among participants who are subjected to the same treatment or condition in an experiment.

Mean Square

A measure used in statistics that represents the average of the squares of the differences from the mean, often used in the context of variance and regression analysis.

Treatments

In the context of experiments, interventions applied to subjects or conditions under study to observe potential changes.

Mean Square

The average of the squared differences from the mean, used in variance and ANOVA calculations.