Question 2 A student determines a potential function for the vector field \(<2 x, x^{\wedge}3>\) as \[ f(x, y)=x^{\wedge}2+y x^{\wedge}3+C \] and concludes that the vector field is indeed a gradient field, with \( f \) as its potential function. If the student is correct, choose True. If the student is incorrect, choose False. True False Question 3 As developed in the lecture, what is the geometric interpretation of the value of a line integral: \(\int f(x, y) d s \)? All answers are in the context of the R3 coordinate system. The length of a curve Difference of areas of a vertical surface Difference of volumes The area of a flat region in the xy-plane