In this lesson, we will learn how to approximate the area under the curve of a function using right, left, and midpoint Riemann sums.
Students will be able to
Q1:
Given that 𝑓(𝑥)=4𝑥cos and that 0≤𝑥≤𝜋4, evaluate, to the nearest six decimal places, the Riemann sum for 𝑓 with six subintervals, taking the sample points to be left endpoints.
Q2:
Let 𝑓(𝑥)=54𝑥 over 1≤𝑥≤2. Using four subintervals and taking midpoints as sample points, evaluate the Riemann sum of 𝑓 to six decimal places.
Q3:
Given 𝑓(𝑥)=𝑥−4 and −4≤𝑥≤2, evaluate the Riemann sum for 𝑓 with six subintervals, taking sample points to be midpoints.
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