Use the Midpoint Rule to Approximate the Given Integral with the Specified

question 104

Multiple Choice

Use the Midpoint Rule to approximate the given integral with the specified value of n. Compare your result to the actual value. Find the error in the approximation. $2 \int_{2}^{3} e^{-\sqrt{x}} d x, \quad n=6$

• A) \(-0.00008\)
• B) \(0.60004\)
• C) 0.00008
• D) 1.00008
• E) \(-0.00096\)

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Definitions:

Hypopharynx

The lower part of the pharynx (throat) that lies below the oropharynx and above the esophagus and larynx, involved in swallowing.

Pharynx

The muscular tube that extends from the back of the nose to the esophagus, part of the digestive and respiratory systems.

Small Intestine

A long, coiled section of the digestive system where most digestion and absorption of nutrients and minerals from food occurs.

Duodenum

The first section of the small intestine, immediately beyond the stomach, that plays a critical role in digestion.