Find the volume of the solid formed by rotating the region enclosed by y=e^(3x)+2, y=0, x=0, x=0.4 about the x-axis.

Answer 1

Volume = π∫(e^(3x) + 2)^2 dx from 0 to .4
= π∫(e^(6x) + 4(e^(3x)) + 4) dx
= π [ (1/6)e^(6x) + (4/3)e^(3x) + 4x] from x=0 to .4
= π[(1/6)e^2.4 + (4/3)e^1.2 + 1.6 - ((1/6) + (4/3) + 0)
= .....

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