Derivative ↔ Integral Explorer

Derivative ↔ Integral Explorer links function height to the tangent slope of accumulated signed area, with all calculations in your browser.

Function

f(x) = sin(x)
A(x) = ∫ₐˣ f(t) dt
A′(x) = f(x)

Anchor a0

Endpoint x1

Function height f(x)

0.8415

Accumulated area A(x)

0.4597

Area-curve slope A′(x)

0.8415

Height becomes a slopeOriginal function

Drag horizontally to move the endpoint. Area colour includes the integration direction.

The accumulated-area curveA(x)Tangent · slope f(x)

At a glance

Accepts: Five continuous presets, an anchor and a movable integration endpoint
Outputs: Signed-area shading and an accumulated-area graph with tangent slope
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 antiderivatives; shading uses sampled cells; reversed bounds reverse the sign
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

For continuous f, A(x) = ∫ₐˣ f(t)dt has derivative A′(x) = f(x). Move the endpoint: the height in the upper graph is the slope of the accumulated-area curve below.

Changing the anchor shifts A vertically but leaves its slope unchanged. When x is left of a, the integration direction reverses, so the signed contributions reverse too.

Reference: the fundamental theorem of calculus

Frequently 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.