Game Physics Engine Development, 2nd Edition

2.2 Calculus 43

2.2.2 Integral Calculus

In mathematics, integration is the opposite of differentiation. If we differentiate

something and then integrate it, we get back to where we started.

In the same way that we obtained velocity from the position using differentiation,

we go the other way in integration. If we know the velocit y, then we integrate to work

out the position at some point in the future . If we k now the accel eration, we can find

the velocity at any point in time.

In physics engines, the term “integration” refers to updating the position and

velocity of each object in each frame. The chunk of code that performs this opera-

tion is ca ...