1.6: Volume of revolution of an exponential region

4PM1/2/November/2020 — Question 2 · 4 marks

The region enclosed by the curve
y=e3x,y=\mathrm{e}^{3x},
the x\displaystyle x-axis, the y\displaystyle y-axis and the line x=3\displaystyle x=3 is rotated through 360∘\displaystyle 360^\circ about the x\displaystyle x-axis.
Use algebraic integration to find, in terms of π\displaystyle \pi and e\displaystyle \mathrm{e}, the volume of the solid generated.
(4)