Riemann Sums Worksheet
Explore Riemann Sums with this worksheet, covering left, right, and midpoint approximations of definite integrals.
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Riemann Sums: Approximating Area Under a Curve
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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 n = 4 subintervals.
2. Using the same function f(x) = x² + 1 on the interval [0, 4], approximate the area under the curve using a Right Riemann Sum with n = 4 subintervals.
3. For the function f(x) = x² + 1 on the interval [0, 4], approximate the area under the curve using a Midpoint Riemann Sum with n = 2 subintervals.
4. A Left Riemann Sum always underestimates the area under a decreasing function.
True
False
5. As the number of subintervals (n) approaches infinity, the Riemann Sum approaches the exact area under the curve.
True
False
6. A Riemann Sum is an approximation of the under a curve.
7. The width of each subinterval in a Riemann Sum is denoted by .
8. For a function that is increasing on an interval, a Right Riemann Sum will the actual area.