Question

Question #aeba9

Answer 1

`~=0.29` (using a 3 segment right rectangle Riemann sum)

Explanation:

Well, if it doesn't require a specific amount of segments or a specific precision, you can just choose. Using only one segment is still an estimate, albeit a (probably) bad one.

I'm going to pick `3` segments for a right rectangle Riemann approximation.

The general formula for a right-sided rectangle Riemann approximation on the interval `[a,b]` using `n` rectangles is:
`sum_(i=1)^n f(a+iDeltax)Deltax`
where `Deltax=(b-1)/n`

Let's plug in the numbers:
`Deltax=(pi^(1/3)-0)/3=pi^(1/3)/3`
`sum_(i=1)^3 pi^(1/3)/3(cos((ipi^(1/3)/3)^3))`

This is equal to:
`(root(3)picos(pi/27)+root(3)picos((8pi)/27)-root(3)pi)/3~=0.29`