Integrating cubic, quadratic and linear functions

Learn about integration of polynomial functions (cubic, quadratic and linear) and how this relates to finding areas on graphs.

Author and programmer: Ron Barrow

UK Years 12-13, KS5, AS Level Core Mathematics, C1, C2

   
           

Instructions below See also:   Polynomial Graphs Differentiating polynomials

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How to Use this Applet

This applet is designed to help you understand what happens when you integrate linear, quadratic and cubic graphs.
The general cubic has the form: Ax³ + Bx² + Cx + D.
By setting A = 0, you get the quadratic: Bx² + Cx + D.
By setting B = 0 as well, you get the straight line Cx + D.
These curves are drawn in black and their equations given at the top left. Varying A, B, C and D changes the curves.
(Note that if you're in quadratic mode, A no longer is relevant, so clicking it will have no effect. Similarly, in linear mode A and B are not used.)
You can move the two integral limits by clicking and dragging them with your mouse. By playing around you should develop an insight into how the area between the curve and the x-axis is related to the value of the integral. Enjoy!