Question

Calc help. (Will medal)

Hello, I need to find the total distance this particle travled for x = 0 and x = 6. I integrated the velocity to find the postion. I pluged in 6 and 0 to the equation and got 35.2657. I do it on my calculator, I get 6.111. Please help.

Answer 1

\[[\frac{ 2 }{ 3 }(2(x)+3)^{\frac{ 3 }{ 2 }}- \frac{ 2 }{ 3 }(x)^{2}]_{0}^{6}\]

Answer 2

I typed it in my calculator right.

Answer 3

The graph does go negative from [4,6]

Answer 4

Where is the velocity equation that you've integrated?

Answer 5

\[x \sqrt{2x+3} -3x dx\]

Answer 6

Hmm it looks like it goes negative from 0 to 3, not from 4 to 6...

Answer 7

Anyway, if the velocity function goes negative anyway,
then it's telling you that the particle stopped and changed directions.
So you would have to break up your integral at that point.

Answer 8

Oh! I see now! So we have \[\int\limits_{0}^{3}v(x) and \int\limits_{3}^{6}v(x)?\]

Answer 9

Sorry upper limit 4

Answer 10

Since the velocity function is below the x-axis,
the distance is going to come out negative (corresponding to moving backwards).
So I guess we should throw some absolutes on that first integral,\[\large\rm \left|\int\limits_0^3v(t)dt\right|+\int\limits_3^6v(t)dt\]

Answer 11

Ok! Thank you for your time!

Answer 12

np