Final answer:
To evaluate the given line integral over curve C, one must parametrize the curve and integrate the given vector field along it using the parameter. Without more details on curve C, a solution cannot be provided.
Step-by-step explanation:
To evaluate the integral \(\int_C ((2xy - z^2)i + (x^2 + 2z)j + (2y - 2xz)k) \cdot dr\), where C is a simple curve from a given point A to another point B, we should use the line integral concept from vector calculus. The exact path of C is not specified, which might influence the complexity of the problem.
However, typically, the curve can be represented parametrically, and then you would integrate along this parameter. Without the complete definition of curve C, we cannot solve this problem directly.
Nonetheless, to proceed with a line integral, there is a need to parameterize the curve C, determine the vector function \(\mathbf{r}(t)\), and its derivative \(\mathbf{r}'(t)\). You would then substitute these into the integral and integrate with respect to the parameter over the limits matching the points A and B.
your complete question is: 1. Evaluate the following line integral:student submitted image, transcription available belowC ((2xy ? z 2 )i + (x 2 + 2z)j + (2y ? 2xz)k) · dr where C is a simple curve from A(-3,-2,-1) to B(1,2,3).