MVC assignment 2

 

Assignment 2: Multivariate Calculus

Instructions:

Complete the following problems related to Green’s Theorem. Ensure that all steps are clearly shown, and provide proper justifications for each step. Include graphical representations where required. Submit your assignment in a professional format.

Question No. 1

Apply the Green’s theorem to find work done by force 𝑭 = [𝑦³, 3𝑥²𝑦] along curve 𝐶, where 𝐶 is the boundary of triangle having vertices (0, 0), (1,0), and (0,1).

Solution:

Question No. 2

Evaluate ∮_𝐶 (𝑦 − sin 𝑥)𝑑𝑥 + cos 𝑥 𝑑𝑦, where 𝐶 is the triangle in adjoining figure:

 

a) Directly (using line integrals)

b) By using Green’s theorem 

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