Evaluate the Integral $\int f ^ { - 1 } ( x ) d x = x f ^ { - 1 } ( x ) - \int f ( y ) d y , y = f ^ { - 1 } ( x )$

question 184

Multiple Choice

Evaluate the integral.
-Use the formula $\int f ^ { - 1 } ( x ) d x = x f ^ { - 1 } ( x ) - \int f ( y ) d y , y = f ^ { - 1 } ( x )$ to evaluate the integral. $\int \cot ^ { - 1 } x d x$

• A) \(x \cot ^ { - 1 } x - \ln \sin x + C\)
• B) \(x \cot ^ { - 1 } x + \ln \sin \left( \cot ^ { - 1 } x \right) + C\)
• C) \(x \cot ^ { - 1 } x - \ln \sin \left( \cot ^ { - 1 } x \right) + C\)
• D) \(x \cot ^ { - 1 } x - x + C\)

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Profit-Maximizing

The strategy by which an organization sets the price and amount of output to achieve the maximum profitability.

Market Price

The current price at which an asset or service can be bought or sold.

Perfectly Competitive Market

A hypothetical market where all participants are price takers, and goods are perfect substitutes, leading to an efficient distribution of resources.

Average Variable Cost

The average amount of variable cost per unit, calculated by dividing total variable costs by the quantity of output.