Estimate L4 and R4 over [0, 8] for the function f(x) = 2 sqrtx .

Question

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Answer 1

By L4 and R4 I assume that you mean the left and right Riemann Sums with 4 equal subintervals.

If so, then Δx = (8-0)/4 = 2, and f(x) = 2√x.

L4 = f(0)Δx + f(2)Δx + f(4)Δx + f(6)Δx

= 2[2√0 + 2√2 + 2√4 + 2√6]

R4 = 2[2√2 + 2√4 + 2√6 + 2√8]

Evaluate L4 and R4 on your calculator.