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) \(\int \tan ^ { n } x d x = \frac { 1 } { n - 1 } \tan ^ { n - 1 } x + \int \tan ^ { n - 1 } x d x\)

Understand the concept of supply elasticity and how to calculate it using the midpoint formula.

Analyze how elasticity affects government tax revenue and the burden of taxes on producers and consumers.

Recognize the behavioral implications of elasticity in public policy, such as the effectiveness of sin taxes.

Interpret graphical representations of supply and demand curves, including shifts due to tax impositions.

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Definitions:

Composite Methods

Depreciation techniques that combine multiple assets into a single group or pool and apply a uniform depreciation rate to the collective group, irrespective of individual asset life.

Depreciation Expense

Distributing the expense of a physical asset throughout its serviceable duration.

Residual Value

The estimated amount that an asset is expected to realize upon the end of its useful life, after deducting the cost of disposal.