Use The Definite Integral (Riemann Sum) to evaluate integral (2+3x-x^2) where x is from 1 to 5?

Question

The solution should include Δx and xi

Answer 1

Hi Tarik S.,

You could certainly integrate the polynomial to the form 2x + (3/2)x^2 - (1/3)x^3, then take the difference at the limits. Or perhaps only the integers are intended as arguments? If the latter is the case, then you have an analogous case to taking sigma (x=a to b by integers) (f(x)) . That is quite a different beast, and you need open-form polynomials for sigma (x= 1 to n by integers) x^r , applied for each term of the polynomial. The functions aren't difficult, and they have a lovely progression as r increases by units. If you want a bit more on that, comment back and I'll eventually get back to you.

-- Cheers, --Mr. d.