Calculus · Mathematics

Calculus Grapher Simulation

Q: Why does the integral keep growing where f is positive?

The integral is the accumulated area, and positive f adds positive area.

Sketch any function with your finger and see its derivative, second derivative and integral drawn live. Drag a tangent along the curve and watch the area accumulate.

Interactive virtual lab · no download · works on phones and laptops

Chapter: Differentiation · Integration
For: Class 11 · Class 12 · JEE
Time: ~12 min

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How to use it

1Drag on the top graph to push and pull the curve.
2Choose a preset: sine, parabola, step, triangle.
3Turn the derivative, second derivative and integral graphs on and off.
4Drag the reference line to compare values at one x.

What to notice

Where f has a peak or a trough, f′ crosses zero.
Where f is concave up, f″ is positive.
The integral grows where f is above the axis and falls where it is below.
A corner in f becomes a jump in f′.

For teachers

A ready-made teaching kit comes with this lab

Lesson plan
21 min, 4 steps
Ask the class
3 questions with answers
Quick quiz
7 questions, printable
Key formulas
2 formulas

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About the Calculus Grapher simulation

The derivative of a function is the slope of its graph at each point, and the integral is the area under it. Drawing a function together with its derivative and integral shows how they are tied: where f rises, f′ is positive; where f has a peak, f′ is zero; where f′ is positive, the area keeps growing.

In this calculus grapher you draw or push and pull a curve by hand, or start from a preset, and see its derivative, second derivative and integral redrawn instantly, with a tangent line and a running area at a movable marker. It covers Limits and Derivatives in Class 11, Application of Derivatives and Integrals in Class 12, and JEE.

Also covers: derivative, integral, tangent, slope, area under curve, differentiation.