Backwards Derviative? Am i seeing this right?

[1joey1]

Backwards Derviative? Am i seeing this right?

I believe if I am seeing this right, my professor does a backwards derivative in the last step? He didn't quite explain it in class, and I'm going to be attending office hours on monday, if anyone could fill me in on the last step or so I'd be appreciative.

 

[rl.bhat]

It is integration. The rule of integration is,

Int.(x^n) = [x^(n+1)]/(n+1).
It is called backward derivative because

derivative of x^(n+1) = (n+1)*x^n

 

[Ericv_91]

It's an integral, or a backwards derivative as you suggest shown by that fancy squiggly he's got there. Essentially it's used when you're trying to find the area under a curve. In your case the area under the curve is the work in Joules.

When you have to calculate the integral of x^n, the general formula is x(^(n+1))/(n+1). So the integral of the first term 3x^2 becomes 3/3 x^3. For the last term, (+10) its the same as writing 10*x^0 (because x^0 is 1). so plug it into the equation I showed you and you'll get the same answer he got.

 

[1joey1]

Thanks guys i really do appreciate it, my calculus class is about 2 weeks behind my physics class so it's constantly catch-up for me. Thanks and i'll be sure to read into integration this weekend.