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

question 174

Multiple Choice

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

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

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Definitions:

Excess Supply

A scenario in which the market has a supply of a product or service that exceeds the demand for it at its present price.

Quantity Demanded

The total amount of a product or service that consumers are willing to buy at a given price over a specified period.

Price Sunglasses

The amount of money required to purchase eyewear designed to protect the eyes from the sun's harmful rays.

Market Equilibrium

The condition in a market where the quantity supplied equals the quantity demanded, resulting in no surplus or shortage and stable prices.