Approximate the area under the curve y = x ^2 from x = 0 to x = 3 using a Right Endpoint approximation with 6 subdivisions.

Question

Approximate the area under the curve  from  to  using a Right Endpoint approximation with 6 subdivisions.

Answer 1

Right Riemann sum with 6 subdivisions on x = [0,3]. The discrete points are x = 0, 0.5, 1.0,...,3.0. (Δx = 0.5)

Solve for y starting at the second discrete point x = 0.5 because this is a Right Riemann sum.

y = [0.25, 1, 2.25, 4, 6.25, 9.0].

Sum y and multiple by Δx: ∑y = 22.75 x 0.5 = 11.375