Final answer:
The student's question is about evaluating a line integral within a multivariable calculus context by simplifying it into a single-variable integral for computational ease.
Step-by-step explanation:
The student's question pertains to the subject of Mathematics, specifically within the area of vector calculus or multivariable calculus, often taught at the college level. The question requires knowledge of different types of integrals such as line integrals and surface integrals. By the context provided, the student seems to be asking about evaluating a line integral along a certain path, where the integral needs to be reduced to a function of a single variable, either x or y.
From the provided information, it appears that the correct approach to this problem involves converting the dy/dx segment into a one-variable integral, which then allows for the application of standard integration techniques. This approach simplifies the evaluation of the line integral especially when the path is along a curve such as a parabola.
The question seems to touch on a practical application where the choice of variable may simplify the calculation, and illustrates the process through which one would convert a more complex integral into a more manageable form. This exemplifies typical problem-solving strategies in higher-level calculus courses.