Calc Help

[Killerme33]

Sorry, I really hate to ask for calculus help here, but I have 30+ attempts on this problem and emailing the professor didn't really help.

The Problem:
A particle that moves along a straight line has velocity v(t)=t^2 * e^-3t meters per second after t seconds. How many meters will it travel during the first t seconds?

Here is my work so far, the S is the integral sign:

u=t^2 dv=e^-3t
du=2t v= -1/3 e^-3t

when I do uv-Svdu I get:
2t * -1/3 e^-3t - S(2t*-1/3 e^-3t)

Bringing the terms out front I get:
2t * -1/3 e^-3t + 2/3 S(t*e^-3t)

I integrate by parts again, but this time letting:
u=t dv=e^-3t
du=1 v=-1/3 e^-3t

So my formula becomes:
2t * -1/3 e^-3t + 2/3 (t*-1/3 * e^-3t - S (-1/3 e^-3t))


Bring out the terms once again:
2t * -1/3 e^-3t + 2/3 (-t/3 e^-3t + 1/3 S (e^-3t)

Integrate the last part and I get:
2t * -1/3 e^-3t + 2/3 (-t/3 e^-3t + 1/3(-1/3 e^-3t))

So my final answer becomes:
-2t/3 * e^-3t + 2/3 (-t/3 e^-3t - 1/9 e^-3t)

Thanks!

 

[Tiamat]

I got -1/27 (e^-3t) (9t^2 + 6x + 2)

I will pm you the soln so you can find your simple mistakes. Deals with multiplying fractions lol

 

[JohnCU]

more algebra than calculus

 

[Tiamat]

Originally posted by: JohnCU
more algebra than calculus

Thats a common problem these days

People are great with calculus but suck it up with the algebra. Very sad

OP, you just need to work very slowly and make sure you don't make silly mistakes

 

[JohnCU]

Originally posted by: Tiamat

Originally posted by: JohnCU
more algebra than calculus

Thats a common problem these days

People are great with calculus but suck it up with the algebra. Very sad

OP, you just need to work very slowly and make sure you don't make silly mistakes

true, my circuits professor used to say, "the EE is done" after we'd get the loop/nodal equations down, then focus on the algebra.