Integral Calculator

Visualize definite integrals and Riemann sums with multiple approximation methods

Overview

The Integral Calculator provides an interactive visualization of definite integrals as areas under curves. Explore different numerical integration methods including left, right, midpoint, and trapezoidal Riemann sums, and see how they converge to the true integral value.

Tips

1. Increase the number of rectangles to watch approximations improve and converge to the exact integral value
2. Compare approximation methods - midpoint and trapezoidal typically give more accurate results with fewer rectangles than left or right methods
3. Notice over/underestimation patterns - for increasing functions, left sums underestimate while right sums overestimate
4. Use the trapezoidal rule for smooth functions as it often provides the best balance of accuracy and computational efficiency
5. Experiment with different functions to see how the choice of approximation method affects accuracy for various curve shapes