Area between a curve and a line with integrals

[heartshapes]

I have been stuck on this problem for quite awhile.

Find the area of the regions enclosed by the lines and curves anyway you can.
- The line y=x and the curve y=x[sup:3yey7m6h]3[/sup:3yey7m6h]-2x[sup:3yey7m6h]2[/sup:3yey7m6h]-3x+1 (hint: there are two regions)

I found that the points of intersection are (.22713444,.22713444) and (3.1642479,3.1642479).

I tried it different ways, and the highest answer I got was around 14.

The back of the book says the answer is 15.68376.

Any help would be great!

Thanks -

 

[tkhunny]

How did you miss the intersection at (-1.391,-1.391)?

\(\displaystyle \int_{-1.391}^{0.227}(x^{3}-2x^{2}-3x+1)\;-\;x\;dx\;+\;\int_{0.227}^{3.164}x\;-\;(x^{3}-2x^{2}-3x+1)\;dx\)

Sure enough. I get 15.684.

More importantly, why are you getting different answers? Are you just being careless or is there something else going on?

 

[heartshapes]

Wow thanks so much.

I did miss that intersection. My window was cut off at -1. I will have to make sure to make it bigger next time!

I was getting the wrong answer because I was doing the x-axis to .227, then .227 to 3.16, not -1.39 to .227 and .227 to 3.16.

Thanks a lot!

 

[tkhunny]

Word to the wise student. Cubic equations have 3 solutions. Don't give up after 2. Good work.