Set Up, but Do Not Evaluate, an Integral for the Area

question 54

Multiple Choice

Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the given axis. $y=e^{x}, 1 \leq y \leq 9 ;$ y-axis

• A) \(\int_{1}^{9} 2 \pi x \sqrt{1+e^{2 x}} d x\)
• B) \(\int_{1}^{9} 2 \pi x e^{9 x} \sqrt{1+e^{9 x}} d x\)
• C) \(\int_{0}^{\ln 9} 2 \pi x \sqrt{1+e^{2 x}} d x\)
• D) \(\int_{1}^{9} 2 \pi \sqrt{1+e^{2 x}} d x\)
• E) \(\int_{0}^{\ln 9} 2 \pi x \sqrt{1+e^{9 x}} d x\)

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Definitions:

Prolonged Labour

A condition in childbirth where labor lasts for a significantly longer duration than is typically expected, possibly leading to complications.

Fetal Distress

A condition in which a fetus is not well or is experiencing stress during pregnancy, often indicated by abnormal heart rate patterns detected during labor.

Birth Complication

Any problem that occurs during the birth process, potentially affecting the health of the mother or child.

Bizarre Delusion

A false belief that is strange, completely implausible, and not rooted in reality, often seen in severe mental disorders.