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:

Ilium

The largest of the three bones making up the pelvis, contributing to the hip joint.

Acetabulum

Cup-shaped depression on the external surface of the coxa.

Articulates

Refers to two or more bones that connect in a joint, allowing for various degrees of movement or stability in the skeleton.

Femur

The thigh bone, which is the longest, largest, and strongest bone in the human body, connecting the hip to the knee.