00:01
So in this question we are looking for an integral, which is the integral along a curve c of x, y, z squared, ds, where c is the line segment from minus 3, 3, 0, to minus 1, 4, 3.
00:18
So first of all, we know that x on c is minus 3 plus 2t for t in the interval 0 to 1.
00:28
Y on c is 3 plus t for t in 0 to 1, and z on c is 3t for t in 0 to 1.
00:41
Now ds is the square root of dx squared plus dy squared plus dz squared, which is the square root of dx by dt squared plus dy by dt, squared plus dz by dt squared plus dz by dt squared times dt, which is the square root of 4 plus 1 plus 9 d t so this is 5 plus 9 is 14 so root 14 d t.
01:17
Okay so now we can do this integral our integral is the integral from t is 0 to 1 of we've got root 14 from the measure and then we've got x y z squared so that's minus 3 plus 2t, we've got y which is 3 plus t, and we've got z which is 3t, and that's squared.
01:45
So now we can expand stuff out...