posted by christina .
The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles.
A = lim n → ∞ [f(x1)Δx + f(x2)Δx + . . . + f(xn)Δx]
Use this definition to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.
f(x) = 7x cos(7x), 0 ≤ x ≤ π/2
well, you have the formula, so plug in
xi = 0 + k(pi/2)/n
Δx = (pi/2)/n
sum over k=0..n