# Homework Help: Indefinite Integration problem

1. Jul 4, 2011

### QuarkCharmer

1. The problem statement, all variables and given/known data
A particle is moving with the given data. Find the position of the particle.
$a(t)=t^{2}-4t+6$,
$s(0)=0$,
$s(1)=20$

2. Relevant equations

3. The attempt at a solution
$a(t)=t^{2}-4t+6$, $s(0)=0$, $s(1)=20$
$$v(t)=\int t^{2}-4t+6 dt$$
$$v(t)=\frac{t^{3}}{3}-2t^{2}+6t+C_{1}$$
Then I suppose I take the antiderivative again to get to s (distance), I can't solve for the constant yet.

$$s(t)=\int \frac{t^{3}}{3}-2t^{2}+6t+C_{1} dt$$
$$s(t)=\frac{t^{4}}{12}-\frac{2t^{3}}{3}+3t^{2}+C_{1}t+C_{2}$$

So now I have two constants in there? Would I just use the parameters $s(0)=0$ and $s(1)=20$ to try to solve this like a system of 2 equations with two unknowns? I don't really know how to proceed. The other problems like this at least gave me a value for the first derivative of the original function so I could sort of work backwards.

Last edited: Jul 4, 2011
2. Jul 4, 2011

### ideasrule

This is exactly what you do. Be more confident!