Find the volume of the solid formed by rotating the region enclosed by y=e^(2x)+3 y=0, x=0, x=0.9 about the x-axis.

Answer 1

Vol = π[integral] y^2 dx from 0 to .9

y^2 = e^(4x) + 6e^(2x) + 9

so Vol = π[integral] (e^(4x) + 6e^(2x) + 9) dx
= π ( (1/4)e^(4x) + 3e^(2x) + 9x) from 0 to .9
= ...

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