Evaluate the Integral To Evaluate the Integral $\int \sin ^ { - 1 } x d x$

question 98

Multiple Choice

Evaluate the integral.
-Use the formula $\int \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \mathrm { dx } = \mathrm { xf } ^ { - 1 } ( \mathrm { x } ) - \int x \left( \frac { \mathrm { d } } { \mathrm { dx } } \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \right) \mathrm { dx }$ to evaluate the integral. $\int \sin ^ { - 1 } x d x$

• A) \(x \sin ^ { - 1 } x + \sqrt { 1 - x ^ { 2 } } + C\)
• B) \(x \sin ^ { - 1 } x + x + C\)
• C) \(x \sin ^ { - 1 } x + \frac { 1 } { \sqrt { 1 - x ^ { 2 } } } + C\)
• D) \(x \sin ^ { - 1 } x - \sqrt { 1 - x ^ { 2 } } + C\)

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Definitions:

Preexisting Schema

A cognitive framework or concept that helps organize and interpret information, based on prior experiences and knowledge.

Prior Expectations

Presumptions or beliefs about future events or outcomes, formed based on past experiences or acquired knowledge.

Radically Disconfirms

A term that appears to indicate a strong or complete contradiction of expectations or beliefs, potentially leading to a change in those beliefs.

Sentence-Unscrambling Task

A cognitive task used in psychological experiments where participants must rearrange words to form correct sentences, often used to study priming effects.