Question

What is the mathematical process to convert the limiting sum to integral and evaluate the lift? in a simple 'two dimensional model' for the lift given by a tapered aircraft wing of length h whose cross section shape remains 'similar', a formula was obtained: L = lim(n->∞)∑Li = lim(n->∞)∑L0(1-((ξi)/h))δxi = ∫(0->h)L0(1-(x/h))dx

Answer 1

Here is the full question:
What is the mathematical process to convert the limiting sum to integral and evaluate the lift?
In a simple 'two dimensional model' for the lift given by a tapered aircraft wing of length h whose cross section shape remains 'similar', a formula was obtained:
L = lim(n->∞)∑Li = lim(n->∞)∑L0(1-((ξi)/h))δxi = ∫(0->h)L0(1-(x/h))dx
all the '0's & 'i's should be lower case, the 'lim(n->∞)'s are limit as n goes to infinity, and the '∫(0->h)' is the integral between the interval 0 and h..
L0 is the lift at the thick end of the wing (by the fuselage), and Li is the lift from the cross section of the wing at a point ξi from the fuselage.
(i)what mathematical process converts this limiting sum to the integral?
(ii)evaluate the lift L in the case that L0=h=1
(ii) evaluate ∫(0->1)1(1-(x/1))dx = ∫(0->1)(1-x)dx = (1-(1^2)/2)-(0-(0^2)/2) = 0.5?

Answer 2

I think this would be calculating the Riemann sum and then taking the limit as n tends to infinity.

http://www.dummies.com/how-to/content/the-riemann-sum-formula-for-the-definite-integral.html