Using Riemann Sums to Estimate Area
We will use rectangles to approximate the area under the function f(x)=0.25x^3 + 0.5x + 1, between x=-1 and x=3.
1. How many rectangles are needed to estimate the area to within 0.25 using the right endpoint rule? Using the left endpoint rule? Using the midpoint rule? 2. Which rule seems to give the best estimate? Why do you think that might be? 3. The trapezoidal rule for a given value of n is equal to . Use the trapezoidal rule for n=5, n=20, and n=50 and compare it to the left endpoint, right endpoint, and midpoint rules.