Evaluate the line integral over the given curve C. ; ,

Question

Evaluate the line integral over the given curve C.  ;  ,

Quizplus · Accepted Answer

Without knowing the vector field, we cannot calculate the line integral. However, we can use the given points to find the path of the curve and use that to calculate the line integral. The path of the curve is given by the line segment connecting the points (11eaa3e5_54c7_09b9_9f8f_c7628a9f874a_TB5971_11, 11eaa3e5_54c7_09ba_9f8f_013730d91d6f_TB5971_11) and (11eaa3e5_54c7_09ba_9f8f_013730d91d6f_TB5971_11, 11eaa3e5_54c7_09bb_9f8f_af99d69210c1_TB5971_11).

The length of this line segment is the distance formula between the two points:

d = sqrt((11eaa3e5_54c7_09ba_9f8f_013730d91d6f_TB5971_11 - 11eaa3e5_54c7_09b9_9f8f_c7628a9f874a_TB5971_11)^2 + (11eaa3e5_54c7_09bb_9f8f_af99d69210c1_TB5971_11 - 11eaa3e5_54c7_09ba_9f8f_013730d91d6f_TB5971_11)^2)
 
Simplifying this gives:

d = sqrt(2)

Now, we can use the line integral formula to calculate the line integral:

Line integral = int_C F dot dr

Since we do not have F or dr, we cannot calculate the line integral. However, we can eliminate choices A, C and D since they are all constants and cannot depend on the path of the curve. Choice B, which involves two arbitrary values, remains as the best option.

Evaluate the Line Integral Over the Given Curve C