Riemann sum approximation of the area under the curve f(x) = 4x - (1/2)x² on the interval [2, 5] using three subintervals.

Graph of the function f(x) = 4x - (1/2)x² with shaded area under the curve from x = 2 to x = 5, showing Riemann sum approximation using three subintervals.

JPG 320×180 10.4 KB Free · Personal Use

Quality Assured by Worksheets Library Team

Reviewed for educational accuracy and age-appropriateness

ID: #386763

✨ Generate New Worksheet

⭐

Show Answer Key & Explanations Step-by-step solution for: Calculus AB/BC - 6.2 Approximating Areas with Riemann Sums

▼

- The function is $f(x) = 4x - \frac{1}{2}x^2$ on the interval $[2, 6]$.
- The interval width is $6 - 2 = 4$, and with 2 subintervals, each has width $\Delta x = \frac{4}{2} = 2$.
- For the Left Riemann Sum, evaluate $f(x)$ at the left endpoints: $x = 2$ and $x = 4$.
- Calculate $f(2) = 4(2) - \frac{1}{2}(2)^2 = 8 - 2 = 6$.
- Calculate $f(4) = 4(4) - \frac{1}{2}(4)^2 = 16 - 8 = 8$.
- The Left Riemann Sum is $\Delta x \cdot [f(2) + f(4)] = 2 \cdot (6 + 8) = 2 \cdot 14 = 28$.
- For the Right Riemann Sum, evaluate $f(x)$ at the right endpoints: $x = 4$ and $x = 6$.
- Calculate $f(6) = 4(6) - \frac{1}{2}(6)^2 = 24 - 18 = 6$.
- The Right Riemann Sum is $\Delta x \cdot [f(4) + f(6)] = 2 \cdot (8 + 6) = 2 \cdot 14 = 28$.

Parent Tip: Review the logic above to help your child master the concept of riemann sum worksheet.

Print Download

How to use

Click Print to open a print-ready version directly in your browser, or use Download to save the file to your device. The ⭐ Answer button generates an AI answer key instantly - useful for teachers who need a quick reference. Need a different version? Our AI Worksheet Generator lets you create a custom worksheet on any topic in seconds.

Related worksheets: riemann sum worksheet