Evaluate the Line Integral Over the Given Curve $C$ $$\int _ { C } \left( 6 x + 2 y ^ { 2 } \right) d s ; C : \mathbf { r } ( t ) = ( t - 6 ) \mathbf { i } + t \mathbf { j } , 0 \leq t \leq 1$$

question 30

Multiple Choice

Evaluate the line integral over the given curve $C$ .
$$\int _ { C } \left( 6 x + 2 y ^ { 2 } \right) d s ; C : \mathbf { r } ( t ) = ( t - 6 ) \mathbf { i } + t \mathbf { j } , 0 \leq t \leq 1$$

• A) 28
• B) \(- 26\)
• C) \(40 \sqrt { 2 }\)
• D) \(- \frac { 97 } { 3 } \sqrt { 2 }\)

---

Definitions:

Consolidated Equipment

Assets combined from separate entities under a single owner, often seen in financial statements.

Outstanding Stock

Shares of a company's stock that have been issued and are currently held by investors, excluding shares held by the company itself.

Building

A structure with a roof and walls, such as a house or factory, constructed as a place of business, residence, or for other uses.

Cash

Liquid assets held by a company or individual, used for transactions or as a reserve for future payments.