Acceleration of a brick, involving integrals

[majormaaz]

Homework Statement

A 15 kg brick moves along an x axis. Its acceleration as a function of its position is shown in Fig. 7-32. What is the net work performed on the brick by the force causing the acceleration as the brick moves from x = 0 to x = 8.0 m?

Homework Equations

W = FΔx = max

The Attempt at a Solution

I haven't taken calculus prior to the class(am taking it now), and I was just introduced to integrals today by a friend. He showed me how to integrate another Work problem, where F = -6x. I understood that it would integrate into -3x² + C, and I found C. My question is how would I go about this one?

Would I start as ∫F dx = ∫ (15 kg)a dx
W = ∫ 15a dx
W = 15ax
W = 15ΔaΔx ... I'm guessing this is what I should do...
W = 15(24)(80) = 2400 J

But apparently that's wrong.
I would be soooooo thankful for anyone to help me with the integration process from here.

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And just in case anybody tells me to ask my teacher for help, I asked both my Physics C teacher AND my calc teacher, but both refused.

 

[Saitama]

There is no picture in your post.

 

[majormaaz]

haha... The only thing I forgot.
http://www.webassign.net/hrw/07_33.gif
hopefully you can see it.

 

[nasu]

You don't need to know integration techniques. It is enough to understand that the value of the (definite) integral of a function represents the area under the graph of the function.
Here is a lot more straightforward to calculate the area (as all the segments are straight lines).

 

[majormaaz]

oh, wow. I'm an idiot.
I made a typo in typing the url of the picture
here's the correct one:
http://www.webassign.net/hrw/07_34.gif
perhaps I should start using Ctrl C more often...

 

[majormaaz]

I mean, it seems rudimentary that the net work is the area under the curve times mass, since
the area under the curve is aΔx, and multiplying by m gives you maΔx, which equals work.
And yet, that was wrong.

 

[nasu]

So did you get the right answer with the new figure or not? I don't understand.

 

[majormaaz]

ahh... I just viewed the answer key. It has 1200 J, while I kept getting 2400 J.
I think I just forgot to throw the 1/2 in there. Damn. A point lost.
But thanks for helping anyways!