Why bother with learning calculus?

Calculus is the maths of change. This sounds familiar;

In mechanics changing distances, velocities etc... 

In motor sport Integration would be the sum of momentum over time to find the kinetic energy. This could help with working out how to optimise energy. Differentiation would be maximum and minimum points in the laps of variables

In economics integration could be the sum of your savings. Differentiation could be a maximum or a minimum of a stock market. Then buy at a low to sell for profit and knowing when the markets about to drop from a maximum. Game theory revolutionised this though.

The most beautiful thing about calculus is that it can take you to space. To get to the moon first you have to accelerate very quickly to be higher than the escape velocity (first change). The mass of the rocket decreases as the fuel is burnt at a rate (second change). The rocket then slower down after escaping (third change). The gravitation pull from the Earth decreases and the Moon pull increases (fourth and fifth change). Opposite for the return journey.

The gravitational change can be demonstrated for a particle with F=ma in quite a nice way. 

Try to think of other changes!