Find the volume of revolution when the curve defined by y=xe^(2x) is rotated 2*pi radians about the x-axis between x=0 and x=1

This is a standard question that may be found in a C4 mathematics paper. Students should use knowledge of the volume of revolution formula V = piint_{a}^{b} y²dx to find the expression V = piint_{0}^{1} (x²e^4x) dx.
Using the integration by parts formula (below), one can yield an intermediary equation, namely V = pi*[e⁴/4-(1/2)int_{0}^{1} (xe^4x)]. Application of the integration by parts formula again solves the second integral of xe^4x, and substituting in the limits of 0 and 1 yields a final answer of: (pi/32)(5e⁴-1).

Integration by parts formula: int(uv') = uv - int(u'v).