Evaluate the Line Integral $\int _ { C } e ^ { x ^ { 2 } y ^ { 2 } z ^ { 2 } } d x + \sin ( x y z ) d y + \ln ( 1 + x y ) d z$

question 175

Short Answer

Evaluate the line integral $\int _ { C } e ^ { x ^ { 2 } y ^ { 2 } z ^ { 2 } } d x + \sin ( x y z ) d y + \ln ( 1 + x y ) d z$ where $C$ is the line segment from $( 0,0,0 )$ to $( 0,0,1 )$

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Definitions:

Rectus Abdominis

The rectus abdominis is a long muscle that extends along the front of the abdomen, known for its role in flexing the lumbar spine and helping to create a "six-pack" appearance.

External Oblique

A muscle located on the lateral part of the abdomen, part of the abdominal wall muscles, that aids in rotation and lateral flexion of the torso.

Internal Oblique

A muscle in the abdominal wall that lies below the external oblique and just above the transverse abdominal muscles, functioning to rotate and turn the trunk.

Lateral Leg Muscles

Muscles located on the outside part of the leg, involved in movement and stabilization of the leg.