Consider the rotation field F = (-y,x) and the three paths shown in the figure. Compute...

Transcribed Image Text:

Consider the rotation field F = (-y,x) and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line (0, 1) integral F.1 F•T ds is independent of the path, where C is a path from (1,0) to (0,1)? (1, 0) x What is the value of the line integral for the path C, ? (Type an exact answer, using T as needed.) What is the value of the line integral for the path C2, which is a quarter of the unit circle centered at the origin? (Type an exact answer, using t as needed.) What is the value of the line integral for the path C3? (Type an exact answer, using t as needed.) Does it appear that the line integral is independent of the path? Yes O No Consider the rotation field F = (-y,x) and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line (0, 1) integral F.1 F•T ds is independent of the path, where C is a path from (1,0) to (0,1)? (1, 0) x What is the value of the line integral for the path C, ? (Type an exact answer, using T as needed.) What is the value of the line integral for the path C2, which is a quarter of the unit circle centered at the origin? (Type an exact answer, using t as needed.) What is the value of the line integral for the path C3? (Type an exact answer, using t as needed.) Does it appear that the line integral is independent of the path? Yes O No