calc question *area of region bounded by given graph

[chica2006]

Hi, I need help with this question ... I went wrong somewhere along the road but I'm not sure where.

Question: Find the area bounded by the given graphs:
y=x+2, y=x^2

here is the solution I have:
x+2=x^2
x^2-x-2=0
(x+1)(x-2)=0

therefore (-1,2)

= [integral] 2 -1 [(x+2)-x^2]dx
= [integral] 2 -1 (-x^2 + x +2) dx
=[-x^3/3 + x^2/2 +2x] 2 -1
=[-(2)^3/3 +2^2/2 + 2*2]-(-(-1)^3/3 + (-1)^2/2 + 2*(-1)]
=(-8/3+4/2+4)-(1/3+-1/2 -2)
=-9/3 +5/2 + 6
=-18/6 + 15/6 + 6
= 11/2
*this is wrong according to back of text should be 9/2
*** help

 

[royhaas]

Just check your arithmetic. The integration is OK.

 

[chica2006]

maybe I'm blind but can't see where arithmitic went wrong. Is it a problem w/neg or pos?? not sure .. help I can't see it

 

[tkhunny]

+ (-1)^2/2 > 0

If it were me, I'd work on the notation. It will help you if you let it. Very sloppy. Simplify as you go. There is no need to retain everything up to the end. Can you even imagine understanding this section, "]-(-(-1)^3/3", without a very careful examination? Have you EVER seen three negative signs stacked up like that? Simplify, please.