# Concept question on using integrals to find displacement!

1. Jan 19, 2009

1. The problem statement, all variables and given/known data

I was reading a solution to the following question:

Given v(t) = 22 + 18 t, use calculus to determine the total displacement from t initial= 1.5 s to t final = 3.1 s

2. Relevant equations

Here are the steps in the equation:

I get everything up to the last part, where we take get (3.1^2 - 1.5^2)... Why is that we don't do (3.1-1.5)^2 instead? I had always imagined the it would be $$\Delta$$t squared, so just final minus initlal, then squaring the result, and not the final time squared minus initial time squared.

Would be great if you guys could clear up my confusion.

2. Jan 20, 2009

### Dick

Then you imagined wrong. (3.1^2 - 1.5^2) is right, (3.1-1.5)^2 is wrong. If you've done a lot of integrals with a lower limit of 0, you might have gotten that feeling. But it's not correct.