## anonymous 4 years ago A particle that moves along a straight line has velocity (see below) meters per second after t seconds. How many meters will it travel during the first t seconds?

1. anonymous

$v(t)=t^2e ^{-3t}$

2. anonymous

integrate

3. anonymous

I know that, but I might need a little help on the steps.

4. Rogue

$Displacement = \int\limits_{0}^{t} t ^{2} e ^{-3t}dt$

5. anonymous

Remember that $v(t)=\frac{dx(t)}{dt}$

6. anonymous

If you integrate like kristal said: $x(t)=\int_0^tv(t)dt$

7. Rogue

$Distance = \int\limits_{0}^{t}\left| t ^{2} e ^{-3t} \right| dt$

8. anonymous

Do you need help to solve that integral?

9. anonymous

I do, I know it's integration by parts. But I don't know which to make f(x) or g(x).

10. Rogue

$\mu = t ^{2}, d \upsilon = e ^{-3t}$

11. Rogue

I think, following LIPET.