Evaluate $\int _ { C } y z d y + x y d z$

question 3

Multiple Choice

Evaluate $\int _ { C } y z d y + x y d z$ , where $C$ is given by $x = 10 \sqrt { t } , y = 3 t , z = 10 t ^ { 2 } , 0 \leq t \leq 1$ . Round your answer to two decimal place.

• A) \(194.93\)
• B) \(193.93\)
• C) \(195.93\)
• D) \(196.93\)
• E) \(197.93\)

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Definitions:

Slate

A fine-grained, foliated metamorphic rock derived from shale, characterized by its ability to split into thin, durable layers, commonly used in roofing and flooring.

Fault Scarp

A step in the landscape caused when fault movement offsets Earth’s surface.

Columnar Joints

Distinctive polygonal shapes formed in volcanic rock due to contraction as it cools, creating pillar-like formations.

Cleavage

The tendency of a mineral to break along flat, even surfaces as determined by the structure of the mineral’s crystal lattice.