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

question 242

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. $\int \cos ^ { - 1 } x d x$

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

---

Definitions:

Median

In statistics, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

Distribution

In statistics, the way in which values of a variable are spread or dispersed across a range, often visualized through a graph.

Variation

Variation refers to the differences or deviations seen within populations, individuals, or data points, often contributing to biodiversity and uniqueness.

Central Tendency

A statistical measure that identifies a single value as representative of an entire distribution, aiming to provide an accurate description of the entire data set.