HW #04

Due: 09/27/2023

Note: If you have not registered on the web, your hw paper is NOT graded.

Submission Instructions: (Important! If you do not follow them, your paper is not graded.)

• Template (word file)

• One page for each problem (a total of 2 pages). 50 % Penalty if not followed.

• Make a single PDF file. File name: hw_04_doe_john.pdf.

• Email the PDF file to me5331exam@gmail.com with the subject line: Doe, John, HW#4

---

1. Evaluate

I ≡ ⌠ ⌡ 1 0  ⌠ ⌡ √y y  x ey/x d x d y.

by changing the order of the integration.

2. If you make a circle and a square from a string of 1 m and want to minimize the total area, how would you divide the string ? You must use the Lagrange multiplier method.