Grade 11 Riemann Sum Worksheet
Explore Riemann sums for approximating definite integrals with this Grade 11 math worksheet, covering left, right, and midpoint Riemann sums.
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Standards
Riemann Sums: Approximating Area Under a Curve
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Read each question carefully and show all your work. Use the given functions and intervals to calculate the Riemann sums as specified.
1. Estimate the area under the curve f(x) = x² + 1 from x = 0 to x = 4 using a left Riemann sum with 4 subintervals.
2. Calculate the right Riemann sum for g(x) = 1/x on the interval [1, 5] with 4 subintervals.
3. Approximate the area under h(x) = sin(x) from x = 0 to x = π using a midpoint Riemann sum with 2 subintervals.
4. Which of the following is true regarding Riemann sums?
Left Riemann sums always overestimate the area.
Right Riemann sums are always more accurate than left sums.
As the number of subintervals increases, the Riemann sum approaches the exact area.
Midpoint Riemann sums always underestimate the area.
5. A Riemann sum is an approximation of the area under a curve by dividing it into a series of .
6. The width of each subinterval in a Riemann sum is denoted by .
7. The definite integral of a function can be exactly calculated using a Riemann sum with a finite number of subintervals.
True
False