Let \[ A = \int_0^1 \sqrt{1-x^3} \, dx, \quad B = \int_0^1
\sqrt{1-x^4} \, dx, \quad C = \int_0^1 \sqrt{1+x^5} \, dx. \]
Order the numbers \(0, 1, 2, A, B, C\) in ascending order.

Answer: \( 0 < A < B < 1 < C < 2 \).

Mid Level Problem

A box with an open top is to be made from a rectangular
piece of cardboard with dimensions 20 in. by 35cm. by cutting out equal sqaures of
side \(x\) at each corner and then folding up the sides. Express the volume \(V\) of the
box as a function of \(x\). Express the function and variable \(x\)
in terms of inches.

Answer: \( V(x)=x(20-2x)(7.87-2x), \; 0 < x < 3.935\).

Math Triva Question

Leonardo Pisano Bigollo; better known as Fibonacci, modeled the famous fibonacci sequence
after the growth in population of which animal?