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

question 278

Multiple Choice

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

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

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The phenomenon where production costs per unit increase as an operation scales up, typically due to inefficiencies or increased complexities.

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