Riemann Sum Visualizer
Riemann Sum Visualizer computes and visualizes Riemann sums for a function \\( f(x) \\) over an interval, displaying steps with MathJax and a graph with p5.js.
Riemann Sum Visualizer
Riemann Sum Visualizer computes the Riemann sum for a function \\( f(x) \\) over an interval \\([a, b]\\) with \\( n \\) subintervals, using left, right, or midpoint methods. It displays computational steps with MathJax and visualizes the sum with p5.js. Results are copyable, with sharing and embedding options for calculus students.
Example 1: Riemann Sum for a Quadratic Function
Function: \\( f(x) = x^2 \\).
Interval: \\([0, 1]\\), \\( n = 4 \\), Left Riemann Sum.
Step 1: Define the function and parameters.
\\( f(x) = x^2 \\), \\( [a, b] = [0, 1] \\), \\( n = 4 \\), \\( \Delta x = \frac{1-0}{4} = 0.25 \\).
Step 2: Calculate points.
Points: \\( x_0 = 0, x_1 = 0.25, x_2 = 0.5, x_3 = 0.75 \\).
Step 3: Compute the sum.
\\( S = \sum_{i=0}^{3} f(x_i) \Delta x = [f(0) + f(0.25) + f(0.5) + f(0.75)] \cdot 0.25 = 0.21875 \\).
Step 4: Conclusion.
Left Riemann sum is \\( 0.21875 \\).
Example 2: Riemann Sum for a Linear Function
Function: \\( f(x) = 2x \\).
Interval: \\([0, 2]\\), \\( n = 4 \\), Midpoint Riemann Sum.
Step 1: Define the function and parameters.
\\( f(x) = 2x \\), \\( [a, b] = [0, 2] \\), \\( n = 4 \\), \\( \Delta x = \frac{2-0}{4} = 0.5 \\).
Step 2: Calculate midpoints.
Midpoints: \\( x_0 = 0.25, x_1 = 0.75, x_2 = 1.25, x_3 = 1.75 \\).
Step 3: Compute the sum.
\\( S = \sum_{i=0}^{3} f(x_i) \Delta x = [f(0.25) + f(0.75) + f(1.25) + f(1.75)] \cdot 0.5 = 4 \\).
Step 4: Conclusion.
Midpoint Riemann sum is \\( 4 \\).