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Find the volume of a solid whose base is bounded by y=x+1, and y=x^2-1. Whose cross sections are taken perpendicular to the x-axis and are squares.
I think I got it mostly right but I'm just not 100% sure about the setup of the question, once thats done the actual integrals are generally easy enough to solve.
v=bh
v=((x+1)-(x^2-1))^2
v=(-x^2+x+2)^2
v=x^4-2x^3-3x^2+4x+4
v=∫(-1 to 2)x^4-2x^3-3x^2+4x+4 dx
v=(1/5)x^5+(1/2)x^3-x^3+2x^2+4x (-1 to 2)<---- intersection points
=v(2)-v(-1)
=(10.4)-(-2)
=12.4 not sure if this is correct though.