Fundamental Theorem of Calculus, a.k.a., "integration is opposite to differentiation"
- Author:
- Elliot Malkin
Call the red function "g".
Play with the k slider. The point A (the grid on the right) plots the area of the black shaded region (i.e. the integral of g between 0 and k) against k.
As k increases from 0 to 1, A moves upwards: a distance equal to the area of the blue region.
As k increases from 1 to 2, A moves upwards a similar distance: a distance equal to the area of the green region.
As k increases from 2 to 3, A moves upwards a smaller distance: a distance equal to the area of the yellow region.
As k increases from 3 to 4, A moves upwards a larger distance: a distance equal to the area of the red region.
Can you use this to explain why integration is inverse to differentiation?