estimate the area betweem the graph of f(x)=-x^2+5x and the x axis on the interval [1,5] using a left-hand sum with 4 rectangles of equl width.

Question

estimate the area betweem the graph of f(x)=-x^2+5x and the x axis on the interval [1,5] using a left-hand sum with 4 rectangles of equl width.

Answer 1

Area A ≈ L₄; Δx = (b - a)/n = (5 - 1)/4 = 1; L₄ = ∑₀³((1 + k)² + 5(1 + k))·1 = ((1 + 5) + (4 + 10) + (9 + 15) + (16 + 20))·1 = 80