Find an approximation of the area of the region R under the graph of the function f on the interval [−1, 2]. Use n = 6 subintervals.

Question

Choose the representative points to be the left endpoints of the subintervals.

f(x)=6-x^2

Answer 1

Δx = (2 +1)/6 = 0.5; n = 6

Area A ≈ L₆ = ∑₀⁵[6 - (-1 + 0.5x)²]·0.5 = 15.625