Use the rules of summation to calculate R_100 for the function f(x)=12x-3x^2 on the interval [0,4]. Compare that to the actual value of 32.

Question

Use the rules of summation to calculate R_100 for the function f(x)=12x-3x^2 on the interval [0,4]. Compare that to the actual value of 32.

Any help would be amazing

Answer 1

Δx = (4 - 0)/100 = 0.04.

R₁₀₀ =

L₁₀₀ = ∑₀⁹⁹[12(i·Δx) - 3(i·Δx)²] Δx = ∑₀⁹⁹[12·0.04i - 3(0.04·i)²]·0.04 = 31.9968

Percent error ε = (32 - 31.9968)/32 = 0.0001 = 0.01%.

We used L₁₀₀ for R₁₀₀. For calculations we used TI-84: sta(seq( commands frpm MATH menu