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) \(V = 1.142\)

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Definitions:

Null Hypothesis

A hypothesis that there is no significant difference or relationship between specified populations, which serves as a default position until evidence indicates otherwise.

P-Value

Given that the null hypothesis is presumed correct, it's the likelihood of experiencing test findings that are as extreme or more extreme than actually observed ones.

Test Statistic

A calculated value from sample data, used to decide whether to reject the null hypothesis in the context of a hypothesis test.

Null Hypothesis

In statistical testing, a hypothesis that assumes there is no significant difference or effect, serving as the default assumption to test against.