F(x)=e^(-3x/2)

Question

Let R be the region between the graph of f and the x-axis on the interval 0 to 1 . Find the volume V of the solid of revolution generated by revolving R about the x-axis. Give both exact (symbolic) and approximate (numeric) answers.

Answer 1

Consider a thin vertical slice of width dx.
If we rotate the slice about the x-axis, we get a disk of thinkness dx and area πf(x)^2, so the volume is
πf(x)^2 dx.
Integrate all slices from 0 to 1 gives you
∫πf(x)^2 dx

Hint: I get 0.995... as the volume, and the symbolic answer has a factor of π/3.

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