Calculate the Riemann sum 𝑅(𝑓,𝑃,𝐶) for the function 𝑓(𝑥)=𝑥, the partition 𝑃={1,1.3,1.7,2}, and the sample points 𝐶={1.1,1.5,1.8}.

Question

(Use decimal notation. Give your answer to two decimal places.)

𝑅(𝑓,𝑃,𝐶)=

Answer 1

Multiply f(each sample point) by the width of the interval in which the sample point lies, Then add up those products:

f(1.1)(1.3 - 1) + f(1.5)(1.7 - 1.3) + f(1.8)(2 - 1.7) = (1.1)(0.3) + (1.5)(0.4) + (1.8)(0.3)