Use Integration by Parts to Establish a Reduction Formula for the Integral

question 173

Multiple Choice

Use integration by parts to establish a reduction formula for the integral.
- $$\int \tan ^ { n } x d x , n \neq 1$$

• A) \(\int \tan ^ { n } x d x = \frac { 1 } { n - 1 } \tan ^ { n - 1 } x - \int \tan ^ { n - 2 } x d x\)
• B) \(\int \tan ^ { n } x d x = \tan ^ { n - 1 } x - \frac { 1 } { n - 1 } \int \tan ^ { n - 2 } x d x\)
• C) \(\int \tan ^ { n } x d x = \frac { 1 } { n - 1 } \tan ^ { n - 2 } x - \int \tan ^ { n - 1 } x d x\)
• D) \(\int \tan ^ { n } x d x = \frac { 1 } { n - 1 } \tan ^ { n - 1 } x + \int \tan ^ { n - 1 } x d x\)

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Definitions:

Marginal Cost

The cost added by producing one additional unit of a product or service, a crucial concept for making economic decisions.

Average Total Cost

The total cost divided by the quantity produced, indicative of the cost per unit of output.

Average Fixed Cost

Fixed cost divided by output.

Variable Costs

Expenses that change in proportion to the activity of a business.