MATH 220 4. Compute the following Riemann sums to estimate S In each case n is the number of equal-width subintervals. (

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Math 220 4 Compute The Following Riemann Sums To Estimate S In Each Case N Is The Number Of Equal Width Subintervals 1 (100.8 KiB) Viewed 9 times

MATH 220 4. Compute the following Riemann sums to estimate S In each case n is the number of equal-width subintervals. (a) Left sum, n = 50: GeoGebra Assignment 7: Riemann Sums (b) Right sum, n = 75: (c) Middle sum, n = 100: One advantage of a middle sum is that using the midpoint of each subinterval causes some of the rectangle to extend beyond the graph while the rest comes up short, balancing out to make a better estimate of the area than the left or right sum. The middle sum with 100 rectangles is quite accurate in these cases. (d) Remember, the exact value of (a): (b): 5. Complete the same four tasks for (a): (b): S x³ dx is the limit as the number of subintervals of the Rie- mann sum goes to infinity. Assuming it's a reasonable number, what do you think the exact value is (based on (a) thru (c))? Write your answer as a decimal AND as a fraction in lowest terms. (a): (b): (c): (d): 6. Complete the same four tasks for (c): (d): 7. Complete the same four tasks for (c): (d): 2³ dr. L S x dx. Write your answers below: x dx. Write your answers below: S 24 dx. Write your answers below: Page 3 8. Based on your answers to questions 4 through 7, what is the exact value of [₁ Write your answer as a fraction. x28 dx?