Calculate the Arc Length of the Indicated Portion of the Curve

question 1

Multiple Choice

Calculate the arc length of the indicated portion of the curve r(t) .
- $$\mathbf { r } ( \mathrm { t } ) = \left( 8 + 2 \mathrm { t } ^ { 2 } \right) \mathbf { i } + \left( 2 \mathrm { t } ^ { 2 } - 7 \right) \mathbf { j } + \left( 7 - \mathrm { t } ^ { 2 } \right) \mathbf { k } , - 1 \leq t \leq 2$$

• A) 9
• B) 45
• C) 27
• D) 15

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Definitions:

Common Stock

A form of corporate equity ownership, a type of security that represents ownership in a corporation and a claim on a part of the company's profits or losses.

Par Common Stock

The face or nominal value attributed to a common stock share as specified in the company's charter.

Treasury Stock

Represents shares of a company's own stock that it has reacquired and holds, which are not considered assets and do not have voting rights or pay dividends.

Fair Market

The price at which an asset would exchange between a willing buyer and a willing seller, each having reasonable knowledge of all relevant facts and neither being compelled to buy or sell.