#TITLE_ALTERNATIVE# - NOOR HASMI (NIM : 10109005); Pembimbing : Prof. Dr. Iwan Pranoto, ABRARI
The interests to the problem to determine an optimal shape in mathematics have grown significantly lately, and it has many applications. One of them is in the mechanical system design. This problem is not easy, because it involves many possibilities and it doesnt belong to the finite dimensional optimal problem family. In this report, we investigate on how to determine a family of almost optimal curve shapes that satisfies the given initial and terminal values with fixed length of curve and at the same time it maximizes the area under the curve. Initially we try to search in the set of polynomials and their extensions. We find that a good shape is the fifth degree one. After that, we investigate some better shapes. We find that for any given precision, we can construct a piecewise differentiable functions whose area under it close to the area of the supremum solution.