Evaluate the integral 
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Definitions:
Utility Function
A mathematical representation that ranks an individual's preferences over a set of goods and services, indicating levels of satisfaction.
Min Function
A mathematical function that identifies the smallest value from a set of numbers or inputs.
Income
The money received by an individual or business in exchange for providing labor, producing goods, or investing capital, over a certain period.
Price of X
Refers to the cost or value of an item, product, or variable denoted as "X."
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