Final answer:
Evaluating a line integral often entails choosing a parameter that simplifies the computation, which can depend on the complexity of functions involved when expressed in terms of x or y.
Step-by-step explanation:
To evaluate a line integral parameterized by a certain path, we often need to choose a parameterization that simplifies the calculation. In Example 7.4, the line integral is reduced to an integral over a single variable; this can be either x or y. The choice depends on which variable makes the integral simpler to compute.
In some cases, one variable may involve more complex functions like square roots or fractional exponents. Consider a line integral along a parabolic path; by solving for x and dx in terms of y, we can express the integral solely as a function of y, which may or may not be more convenient depending on the scenario.