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

question 52

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.
$$y = \tan x , 0 \leq x \leq \frac { \pi } { 4 }$$ The choices are rounded to the nearest hundredth. Select the correct answer.

• 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:

TsCl

P-toluenesulfonyl chloride, an organic compound used as a reagent in organic synthesis to introduce tosyl groups.

(R)-Pentan-2-Ol

An optically active form of pentanol where the hydroxyl group is attached to the second carbon atom in the pentane chain.

NaI

Sodium iodide, a salt commonly used in organic chemistry as a source of iodide ions in substitution reactions.

TsCl

Tosyl chloride, a reagent used to convert alcohols into tosylates, making them better leaving groups for nucleophilic substitution reactions.