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

question 4

Multiple Choice

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

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

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Definitions:

Cash Disbursements

Outgoing payments made by a business, often documented in a cash disbursement journal, including expenses, creditor payments, and other financial outflows.

Cost of Goods Sold

Cost of goods sold (COGS) represents the direct costs attributable to the production of goods sold by a company, including materials and labor.

Merchandise Inventories

Goods or products that a company holds for the purpose of sale to customers in the ordinary course of business.

Sales Budget

A detailed plan that estimates future sales, usually expressed in both units and dollars, for a specific period.