Geometry to algebra to calculus in 20 minutes.

Helpful complimentary videos:
Putting cubics in graphing form.
Completing the cube.
Geometric view of integration.
Most important---The relationship between differentiation and integration.
Mistake: (3.001)^3 should have been 27.027009001 to maintain the pattern. Try to spot the overestimating aspect of the .000009001 and you will garner a stronger organic understanding of the limiting process.