The ends of a stiff bar of length 4 slide freely inside a parabolic track (specifically, the parabola ). As they do, the midpoint of that bar traces a curve. Find the area of the region between the parabola and the curve traced by .
Assume that the bar slides infinitely in both directions.
where .
Find .
The above sum can be expressed in the form
where is the imaginary unit and is some positive multiple of 4.
Find .
The integral above has a closed form. Find this closed form.
Give your answer to 3 decimal places.
When is a positive integer, what is the value of