Integral Explorer
Integral Explorer visualizes signed Riemann sums and compares four quadrature methods locally in your browser.
∫ₐᵇ f(x) dx ≈ Σ height × Δx
Selected approximation
Exact signed integral
Absolute error
Interval [-3, 3], Δx = 1.5. Colours show signed contributions.
Compare all four methods · 4 subdivisions
left
Error 0.2117
right
Error 0.2117
midpoint
Error 2.22e-16
trapezoid
Error 0
At a glance
- Accepts
- Five preset functions, ordered interval endpoints, 4–1,000 subdivisions
- Outputs
- Signed rectangle/trapezoid plots, four approximations, exact preset integrals and errors
- Where it runs
- Entirely in your browser, on your device
- What leaves your device
- No calculation inputs are uploaded; standard site usage analytics still apply
- Limits
- Preset functions only; endpoints stay in the plotted domain; approximations use finite subdivisions
- Account
- Not required - there is no sign-up
- Price
- Free, with no watermark and no usage cap
- Made by
- Visrut
- Last updated
- 14 October 2026
What to notice
Each rectangle contributes height × width. Left, right and midpoint rules choose different heights; trapezoids use the average of the endpoint heights.
The integral is signed: regions below zero subtract from regions above zero. A total near zero can hide large positive and negative contributions. The exact reference uses a supplied antiderivative for the selected preset.
Reference: approximating areasFrequently asked questions
Are these symbolic calculators?
These tools teach through supported function presets, exact derivatives and antiderivatives where supplied, and labelled numerical approximations. They do not evaluate arbitrary expressions.
Do calculations leave my device?
All graphs and calculations run locally in your browser. No account or external calculation service is required.