# Distance traveled using integrals

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• Feb 22nd 2013, 12:07 PM
Steelers72
Distance traveled using integrals
Ok, I know what to do (take antiderivative and plug in points from a certain interval) but the final answer i get is 10.5 (which is wrong to the system). Can someone please check my work and let me know the correct answer? it's driving me nuts

My work (the boxes show the antiderivative and the interval from 1 to 0. I know that you have to plug in 1 to the antiderivative and 0 and subtract the two. The same goes for the interval 3 to 1. You then would add the two together):

 3 |t2 + 3t − 4| dt http://www.webassign.net/wastatic/wa...g/integral.gif 0
=
 1 −t2 − 3t + 4 dt http://www.webassign.net/wastatic/wa...g/integral.gif 0
+
 3 t2 + 3t − 4 dt http://www.webassign.net/wastatic/wa...g/integral.gif 1
Antiderivatve= -1/3 t^3 -3/2 t^2 +4t |1 and 0 intervals

Antiderivative= 1/3t^3 +3/2 t^2 -4t | 3 and 1 intervals

Interval 1 subtracted by interval of 0:
[-1/3 (1)^3 -3/2 (1)^2 +4(1)] - [0]

Added with

The interval of 3 subtracted by interval of 1:
[1/3(3)^3 +3/2(3)^2-4(3) ] - [1/3(1)^3 +3/2(1)^2-4(1)
• Feb 22nd 2013, 12:09 PM
Bashyboy
Re: Distance traveled using integrals
I'd advise you to fix your post, seeing as it is indecipherable :)
• Feb 22nd 2013, 12:10 PM
Steelers72
Re: Distance traveled using integrals
Lol my fault. Fixed :D
• Feb 22nd 2013, 08:50 PM
Steelers72
Re: Distance traveled using integrals
anyone?
• Feb 23rd 2013, 03:01 AM
Bashyboy
Re: Distance traveled using integrals
To be frank, I can't see anything amiss with your work.

You have the definite integral split at its proper place, so you'll always get a positive output when you evaluate the definite integral:

$\displaystyle \int_0^1(-t^2-3t+4)dt + \int_1^3(t^2+3t-4)dt$

Likewise, it seems that you proceeded with taking the antiderivative properly:

$\displaystyle \frac{-t^3}{3}- \frac{3}{2}t^2+4t \biggr|_0^1+ \frac{t^3}{3}+ \frac{3}{2}t^2 - 4t \biggr|_1^3$

Perhaps you've just had some sort of arithmetic error.
• Feb 23rd 2013, 06:39 AM
topsquark
Re: Distance traveled using integrals
Quote:

Originally Posted by Steelers72

 3 |t2 + 3t − 4| dt http://www.webassign.net/wastatic/wa...g/integral.gif 0
=
 1 −t2 − 3t + 4 dt http://www.webassign.net/wastatic/wa...g/integral.gif 0
+
 3 t2 + 3t − 4 dt http://www.webassign.net/wastatic/wa...g/integral.gif 1
Antiderivatve= -1/3 t^3 -3/2 t^2 +4t |1 and 0 intervals

Antiderivative= 1/3t^3 +3/2 t^2 -4t | 3 and 1 intervals

You might find it helpful to take a look at our LaTeX forum. It may look hard at the start but it is reasonably easy to learn.

-Dan