Math ( calculus 3 )

Line Integral Practice – Due: Tuesday April 30 at final exam

Write your solutions to evaluate each problem using the best method on a separate piece of paper. Be sure to

show all your work and use correct notation. Please note copying is not allowed. If there is evidence of any

copying whatsoever, you will not receive any credit. This assignment is worth 15 points extra credit.

Evaluate the line integral for the following problems along the given curves.

1. The line integral of 𝑭 = ⟨2𝑥𝑦, 𝑥2⟩; C: 𝒓(𝑡) = ⟨9 − 𝑡2 , 𝑡⟩, 0 ≤ 𝑡 ≤ 3

2. ∮ 3𝑥3𝑑𝑦 − 3𝑦3𝑑𝑥

𝐶 ; C is the circle of radius 4 centered at the origin with clockwise orientation.

3. ∫ 𝑦𝑒−𝑥𝑧

𝐶 𝑑𝑠; C is the path 𝒓(𝑡) = ⟨𝑡, 3𝑡, −6𝑡⟩, for 0 ≤ 𝑡 ≤ ln 8.

4. The line integral of 𝑭 = ⟨𝑥2 − 𝑦2, 𝑥, 2𝑦𝑧⟩;

C is the boundary of the plane 𝑧 = 6 − 2𝑥 − 𝑦 in the first octant.