Find a formula for one function that satisfies these given conditions:
1.) f is continuous on [0,1].
2.) f(0) = f(1) = 0 (exactly).
3.) f(x) is greater than or equal to 0 for [0,1]
4.) The area under the graph of f from 0 to 1 is equal to 1 (exactly).
Calculate the arc length.
Try to find the smallest possible arc length.
Arc Length formula
The Attempt at a Solution
I don't know! I'm completely lost. So far I found the function f(x) = -6x^2+6x gives me an arc length of ~3.249 and satisfies all four conditions. But I'm pretty sure there must be a smaller arc length. Please help me find the smallest possible arc length. Thank you!