Use Any Method to Evaluate the Integral $$\int 5 x \sin ^ { 2 } x d x$$

question 412

Multiple Choice

Use any method to evaluate the integral.
- $$\int 5 x \sin ^ { 2 } x d x$$

• A) \(\frac { 5 } { 2 } x ^ { 2 } - \frac { 5 } { 4 } \sin 2 x - \frac { 5 } { 8 } \cos 2 x + C\)
• B) \(\frac { 5 } { 4 } x ^ { 2 } - \frac { 5 } { 4 } \sin 2 x - \frac { 5 } { 8 } \cos 2 x + C\)
• C) \(\frac { 5 } { 2 } x ^ { 2 } + \frac { \sin ^ { 3 } x } { 3 } + C\)
• D) \(5 x ^ { 2 } - \frac { 5 } { 2 } \sin 2 x - \frac { 5 } { 4 } \cos 2 x + C\)

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Definitions:

Marginal Cost

The variation in overall expenses that occurs with the production of an additional unit.

Total-Cost Curve

A graphical representation showing the total cost of producing different quantities of a good or service.

Marginal Product

The additional output that is gained by employing one more unit of a factor of production.

Average-Variable-Cost Curve

A graphical representation showing how the average variable cost of production changes as the quantity of output is altered.