Evaluate the Line Integral Over the Given Curve $C$ $$\int _ { C } ( 5 x + 4 y ) d s ; C : \mathbf { r } ( t ) = ( t - 5 ) \mathbf { i } + t \mathbf { j } , 0 \leq t \leq 3$$

question 23

Multiple Choice

Evaluate the line integral over the given curve $C$ .
$$\int _ { C } ( 5 x + 4 y ) d s ; C : \mathbf { r } ( t ) = ( t - 5 ) \mathbf { i } + t \mathbf { j } , 0 \leq t \leq 3$$

• A) \(- \frac { 9 } { 2 }\)
• B) \(- \frac { 69 } { 2 } \sqrt { 2 }\)
• C) \(\frac { 231 } { 2 } \sqrt { 2 }\)
• D) \(\frac { 81 } { 2 }\)

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Definitions:

Unconditioned Stimulus

in behavioral psychology, a stimulus that naturally and automatically triggers a response without the need for prior learning.

Conditioned Stimulus

A previously neutral stimulus that, after becoming associated with an unconditioned stimulus, eventually triggers a conditioned response.

Conditioned Response

A learned response to a previously neutral stimulus that has been repeatedly associated with an unconditioned stimulus.

Unconditioned Response

An automatic and innate reaction to a stimulus, not learned through prior experience.