Taking Integrals (1/3)

We practiced taking the derivative earlier in the class. This is how we go from (t,x) graphs to (t,v) graphs to (t,a) graphs. There must be a way to go backwards as well. This is called taking the integral. You saw the graphical way of taking the integral earlier in the course- it is equivalent to the area under the curve up to a time t.

 

In calculus class, you'll learn how to take lots of integrals. The rules for determining the integral of a polynomial are given on the left side of the board in this picture.

 

Just as when we took the areas under the curve... taking the integral only partially gets you the next function. Unlike when one takes the derivative, there is missing information that has to be supplied from something other than math. In class, you will either be told this or you will determine it experimentally. In these examples, you can see that I've told you the initial velocity and initial position of these functions.

 

The next picture will have these integrals worked out. Do the best you can with these and then look at the answers to see how your practice went

Done