Input Parameters
Results
Approximated Sum: --
Actual Integral: --
Absolute Error: --
Note: This is an approximation. Actual integral may differ.
Areas per Subinterval
Visualization
Help
How to Use
- Enter a function in terms of x (e.g., x**2 for x squared).
- Specify the interval [a, b] and number of subintervals N.
- Choose the Riemann sum method.
- Click Calculate to see the approximation and graph.
About Riemann Sums
Riemann sums approximate the area under a curve by dividing the interval into subintervals and summing areas of rectangles or trapezoids.
- Left: Uses left endpoints of subintervals.
- Right: Uses right endpoints.
- Midpoint: Uses midpoints.
- Trapezoidal: Uses trapezoids for better accuracy.
Supported Functions
You can use the following mathematical functions in your expression:
- sin(x) or Math.sin(x) - Sine
- cos(x) or Math.cos(x) - Cosine
- tan(x) or Math.tan(x) - Tangent
- exp(x) or Math.exp(x) or e**x - Exponential (e^x)
- log(x) or Math.log(x) or ln(x) - Natural logarithm
- sqrt(x) or Math.sqrt(x) - Square root
- pi or Math.PI - Pi constant
- e or Math.E - Euler's number
- Arithmetic operators: +, -, *, /, ** (power)
- Parentheses for grouping