Multiple choice

Consider points P and Q in the x - y plane, with P = (1, 0) and Q (0, 1). The line integral 2$\int\limits_P^o (x dx + ydy)$along the semicircle with the line segment PQ as its diameter

  1. is - 1

  2. is 0

  3. is 1

  4. depends on the direction (clockwise or anti - clockwise) of the semicircle
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$I = 2 \int\limits_P^Q (xdx + ydy) \\ = 2 \int\limits_P^Q xdx + 2 \int\limits_P^Q ydy \\ = 2 \int\limits_1^0 xdx + 2 \int\limits_1^0 ydy = 0$

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