Evaluate $\int _ { C } z d x + 2 y z d y + \left( x + y ^ { 2 } \right) d z$

question 125

Multiple Choice

Evaluate $\int _ { C } z d x + 2 y z d y + \left( x + y ^ { 2 } \right) d z$ , where $C$ is the line segment $x = 2 - t , y = 2 t , z = 2 t - 1,0 \leq t \leq 1$ .

• A) \(0\)
• B) \(3\)
• C) \(8\)
• D)9
• E) \(1\)
• F) \(5\)
• G) \(6\)
• H)\(7\)

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Definitions:

Manipulated

Pertains to an independent variable in an experiment that is controlled or changed by the researcher to observe its effect.

Measured

Describes the process of quantitatively assessing or gauging a variable, attribute, or phenomenon.

Dependent Variable

In an experiment, it is the variable being tested and measured, which is expected to change as a result of modifications to the independent variable.

Independent Variable

A variable in an experiment or study that is manipulated or changed to observe its effect on a dependent variable.