use a right-endpoint Riemann sum with n=4 subintervals to approximate the area under a curve f(x)=x^2 on the i

Question

use a right-endpoint Riemann sum with n=4 subintervals to approximate the area under a curve f(x)=x^2  on the interval (0,4)

GPT-5 mini · Answer

Δx = (4−0)/4 = 1. Right endpoints: 1, 2, 3, 4.

Right Riemann sum = Σ f(x_i)Δx = (1^2 + 2^2 + 3^2 + 4^2)·1 = 1 + 4 + 9 + 16 = 30.

(For comparison, the exact area ∫_0^4 x^2 dx = 4^3/3 = 64/3 ≈ 21.33, so the right-endpoint sum here is an overestimate because f is increasing.)

use a right-endpoint Riemann sum with n=4 subintervals to approximate the area under a curve f(x)=x^2 on the interval (0,4)