Summary: Math 103.02 Quiz Ten
Due Monday, November 29.
I have neither given nor received aid in the completion of this test.
Signature:
(1) Let C be the segment joining (1, 1) to (3, 5). Calculate
C
x dx
C
x ds and
C
(x, y) · T ds.
Solution. Let P(t) = (x(t), y(t)) = (1 + 2t, 1 + 4t) , 0 t 1. Then P parame-
terizes C and P (t) = (2, 4), 0 t 1, so
C
x dx =
1
0
(1 + 2t) 2dt = 4 (since dx = 2 dt);
C
x ds =