Riemann Sum Explorer
Interactively approximate definite integrals using left, right, and midpoint Riemann sums. Adjust the number of rectangles to watch the approximation converge to the true area under the curve.
Area Between Two Curves
Visualize and calculate the area between two curves using definite integrals. Explore how to find intersection points, determine which function is on top, and set up the integral ∫[a to b] (f(x) - g(x))dx. Practice with vertical and horizontal slicing methods, and understand applications in physics, economics, and geometry where finding regions between curves is essential.
Riemann Sum Approx
Interactive summation explorer comparing Left, Right, Midpoint Riemann sums and Trapezoidal logic. N-slider rapidly expands bounding box series $\Sigma$ into exact integral space via $N \rightarrow \infty$, dynamically revealing errors algebraically and geometrically.
FTC Accumulation
Fundamental Theorem of Calculus visually represented. Sweeps across $f(t)$ bounds bridging dynamic differential area accumulation natively into the $F(x)$ graphing engine.