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Imagine thin disks perpendicular to the x-axis stacked up between x=-2 and x=-1. The radius of each disk is y=e^(2x) and the thickness is dx. The volume of each disk is πy^2 dx. The sum of the volumes of these disks is
π∫e^(4x) dx integrated from x=-2 to x=-1
= (π/4)e^(4x) where x is evaluated from x=-2 to x=-1
= (π/4)(e^(-4)-e^(-8))
π∫e^(4x) dx integrated from x=-2 to x=-1
= (π/4)e^(4x) where x is evaluated from x=-2 to x=-1
= (π/4)(e^(-4)-e^(-8))