Calculate the Riemann sum 𝑅(𝑓,𝑃,𝐶) for the function 𝑓(𝑥)=𝑥^2+7𝑥, the partition 𝑃={2,6,9,12} and the sample points 𝐶={5,8.5,9.5}.

Answer 1

f(5)(6 - 2) + f(8.5)(9 - 6) + f(9.5)(12 - 9) = 4f(5) + 3f(8.5) + 3f(9.5) =4(60) + 3(131.75) + 3(156.75) = 1105.5

f(5)(6-2) = f(sample point in the first interval)(length of first interval). Do the same for each interval and add the results