Calculus · UNI_FOUNDATION

Integral calculus

Question 1/8+12 XP
Find an antiderivative of . Give one without .
Riemann sumf(x) = 2x², n = 8
012345204060xf(x)Δx = 0.63area
difference 16.28 (too much)
curve fexact area = 83.338 rectangles (right edge) = 99.61
Right-endpoint rule: each of the 8 rectangles is as tall as the curve at the right edge of its strip (width Δx = 0.63). That leaves a visible seam between rectangle top and curve: R₈ = 99.61 against the exact 83.33 — 16.28 too much. More strips shrink that seam to nothing — that passage to the limit is the integral.