Volume of Revolution Problem: Finding the Volume of a Solid of Revolution

[G01]

Find the volume created by revolving:
$$y=x^2 +x - 2$$

and y=0 about the x axis.

$$y=x^2 +x - 2$$ intersects the x-axis at -1 and 1 so those are the bounds of integration.

the radius of the figure = -($$y=x^2 +x - 2$$)

so:

V = $$- \pi \int_{-1}^1 (x^2 + x - 2)^2 dx$$

After integrating that I get 18$$\pi$$/5. The actual answer is 81$$\pi$$/10. What I want to know is if i set the integral up right. If I did then this is only a stupid integration mistake. If not then I hope someone finds my mistake. Thanks for the help.

 

[TD]

$$y=x^2 +x - 2$$ intersects the x-axis at -1 and 1 so those are the bounds of integration.

You may want to check that again
Fix this, and you'll find the given answer.