Evaluate the Integral Using the Given Substitution $\int \sqrt { x } \cos ^ { 2 } \left( x ^ { 3 / 2 } - 6 \right) d x , \quad u = x ^ { 3 / 2 } - 6$

question 93

Multiple Choice

Evaluate the integral using the given substitution.
- $\int \sqrt { x } \cos ^ { 2 } \left( x ^ { 3 / 2 } - 6 \right) d x , \quad u = x ^ { 3 / 2 } - 6$

• A) \(\frac { 1 } { 3 } \left( x ^ { 3 / 2 } - 6 \right) + \frac { 1 } { 6 } \sin 2 \left( x ^ { 3 / 2 } - 6 \right) + C\)
• B) \(\frac { 1 } { 3 } ( \sqrt { x } ) \sin \left( x ^ { 3 / 2 } - 6 \right) + C\)
• C) \(x ^ { 3 / 2 } - 6 + \frac { 1 } { 2 } \sin 2 \left( x ^ { 3 / 2 } - 6 \right) + C\)
• D) \(\frac { 2 } { 9 } \sin ^ { 3 } \left( x ^ { 3 / 2 } - 6 \right) + C\)

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Definitions:

Positive Autocorrelation

A statistical property of a series indicating that values close together in time are positively correlated and tend to move in the same direction.

Durbin-Watson Statistic

A statistical measure employed to identify autocorrelation within the residuals of a regression analysis.

Independence of Errors

An assumption in statistical models indicating that the error terms are not correlated with each other.

Durbin-Watson Test

A statistical test used to detect the presence of autocorrelation in the residuals from a regression analysis.