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Find the volume created by revolving:
[tex]y=x^2 +x - 2[/tex]
and y=0 about the x axis.
[tex]y=x^2 +x - 2[/tex] intersects the x-axis at -1 and 1 so those are the bounds of integration.
the radius of the figure = -([tex]y=x^2 +x - 2[/tex])
so:
V = [tex]- \pi \int_{-1}^1 (x^2 + x - 2)^2 dx[/tex]
After integrating that I get 18[tex]\pi[/tex]/5. The actual answer is 81[tex]\pi[/tex]/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.
[tex]y=x^2 +x - 2[/tex]
and y=0 about the x axis.
[tex]y=x^2 +x - 2[/tex] intersects the x-axis at -1 and 1 so those are the bounds of integration.
the radius of the figure = -([tex]y=x^2 +x - 2[/tex])
so:
V = [tex]- \pi \int_{-1}^1 (x^2 + x - 2)^2 dx[/tex]
After integrating that I get 18[tex]\pi[/tex]/5. The actual answer is 81[tex]\pi[/tex]/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.
