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

question 152

Short Answer

Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve $y = \ln x ^ { 7 }$ about the $x$ -axis on the interval $1 \leq x \leq 7$ .

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Definitions:

Tejanos

People of Mexican heritage who have lived in the territory of the current state of Texas since before it became part of the United States, with a unique culture blending Mexican and Texan influences.

Texians

Residents of the Mexican province of Texas who supported the Texas Revolution against Mexico to achieve independent statehood in 1836.

German Immigration

The movement of German people into the United States, especially significant during the 19th century when they formed one of the largest immigrant groups, influencing American culture and society.

Irish Immigration

The movement of individuals from Ireland to other countries, notably to the United States, often in response to economic hardship, famine, or political unrest.