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13 Nov 2019
Suppose we are estimating the area under the graph of the function f(x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a midpoint Riemann sum with 8 subintervals of equal width, what are the midpoints that we will use? 5. 6. Now suppose f(x)-10-10 Use a midpoint Riemann sum with n = 4 rectangles to estimate the area under the graph of this function and above the x-axis. Repeat the previous question, using a left Riemann sum with n = 6 rectangles. Draw pictures of the rectangles used for exercises 6 and 7, like you see in the Preview Activity for this section. Based on the visuals, which appears to be a better approximation to the true area under the curve: A midpoint sum with 4 rectangles, or a left-hand sum with 6 rectangles? Explain. 7, 8.
Suppose we are estimating the area under the graph of the function f(x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a midpoint Riemann sum with 8 subintervals of equal width, what are the midpoints that we will use? 5. 6. Now suppose f(x)-10-10 Use a midpoint Riemann sum with n = 4 rectangles to estimate the area under the graph of this function and above the x-axis. Repeat the previous question, using a left Riemann sum with n = 6 rectangles. Draw pictures of the rectangles used for exercises 6 and 7, like you see in the Preview Activity for this section. Based on the visuals, which appears to be a better approximation to the true area under the curve: A midpoint sum with 4 rectangles, or a left-hand sum with 6 rectangles? Explain. 7, 8.
Beverley SmithLv2
23 Apr 2019