 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/9/b/solution

On the horizontal segment

y = 0

, while

x

decreases from

1

- 1

. Keeping this orientation gives

\int_{C} F \cdot d r = \int_{1}^{- 1} x^{2} d x = - \frac{2}{3} .

The minus sign follows from traversing opposite to the positive

x

direction.

 New to topics? Read the docs here!