Riemann Sums Worksheet
Explore the concept of Riemann sums to approximate the area under a curve, including left, right, and midpoint sums.
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Riemann Sums Worksheet
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Read each question carefully and show all your work. Use the given function and intervals to calculate the Riemann sums as specified.
1. Consider the function f(x) = x² + 1 on the interval [0, 4]. Approximate the area under the curve using a Left Riemann Sum with 4 subintervals.
2. For the function f(x) = x² + 1 on the interval [0, 4], approximate the area under the curve using a Right Riemann Sum with 4 subintervals.
3. Approximate the area under the curve of f(x) = x² + 1 on the interval [0, 4] using a Midpoint Riemann Sum with 4 subintervals.
4. Which type of Riemann sum typically underestimates the area for an increasing function?
Left Riemann Sum
Right Riemann Sum
Midpoint Riemann Sum
Trapezoidal Sum
5. A Riemann sum is an approximation of the area under a curve by dividing the region into a series of .
6. As the number of subintervals increases, the approximation of the area under the curve using Riemann sums becomes more .
7. For a decreasing function, a Right Riemann Sum will overestimate the true area under the curve.
True
False