Calculus Is So Hard, Or Is It?

Get a friend to through a ball to you. In order to catch it you will estimate its speed and direction (known as velocity) Then carry out a first order integration to determein its position at a later point in time. You will then take account of acceleration due to gravity, wind reistance and possibly side winds. Then carry out a second order integration to factor these things in to the position at a later time. Then by carrying out a first order differentiation you can estimate the balls speed and direction when it reaches you.

All carried out in your head without you realising what you can do