University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

485

Pages:

1
Author:

Charlee Buchanan

Workshop #29 Z 1. Evaluate the line integral y 2 dx, where C is the line connecting the points (−3, −1) and (5, 9). C Z 2. Evaluate the line integral z dx + sin x dy + 3x2 dz, where C : x = t, y = t2 , z = et , 0 ≤ t ≤ 1. C 3. Recall that arc length in the plane is given by Z t0 r s(t0 ) = a dx 2 dy 2 + dt, dt dt and from this we have that r ds dx 2 dy 2 = + , dt dt dt using t as the parameter. Using differentials, we can write this as r dx 2 dy 2 + dt, ds = dt dt and we can integrate a function f (x, y) above a curve C in the plane using r Z b Z b dx 2 dy 2 f (x, y) f (x, y) ds = + dt. dt dt a a This can be extended to higher dimensions. Z Use this to compute C yez ds, where C is the circular helix x = cos t, y = sin t, z = t, 0 ≤ t ≤ 2π.