## swin2013 Group Title A particle starts at x(0) = 2. If its velocity is given by v(t) = ln(1+t), find its position at t = 5 one year ago one year ago

1. campbell_st Group Title

the primitive of v(t) will give the displacement equation x(t) so find the indefinite integral of $\int\limits \ln(1 + t) dt$ you also know that when t = 0, x(t) = 2 so the particle starts 2 units to the right of the origin. you will need to use these to evaluate the constant in the indefinite integral. Lastly, when you have your equation, substitute t = 5 and evaluate to find the postiion from the origin

2. swin2013 Group Title

by u substitution correct? i think i am doing that process wrong

3. campbell_st Group Title

well its a standard integral $\int\limits \ln(ax + b) dx = \frac{(ax + b)}{a} \ln(ax + b) - x + c$

4. swin2013 Group Title

oh that is where i get confused. lol. because i did: y = lnu u = 1+t dy/du = ulnu du/dx = 1 dy/dx = dy/du * du/dx and then i add that to the constant 2.

5. swin2013 Group Title

@zepdrix can you help me? loll maybe i'm thinking waaayy too much into this

6. campbell_st Group Title

you need to use integration by parts so f = ln(u) dg = du df = 1/u du g = u so then you have $uln(u) - \int\limits 1 du$ which gives the integral of uln(u) - u and when u = t + 1 you get - t + (t + 1)(ln (t + 1) - 1) or (t + 1)log(t +1) - 1

7. swin2013 Group Title

AHHH ok thanks :)