Answers>Maths>A Level>Article

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).

Answered by Hanish S. • Maths tutor

4156 Views

See similar Maths A Level tutors

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

Related Maths A Level answers

Consider f(x)=a/(x-1)^2-1. For which a>1 is the triangle formed by (0,0) and the intersections of f(x) with the positive x- and y-axis isosceles?

A curve with equation y=f(x) passes through the point (1, 4/3). Given that f'(x) = x^3 + 2*x^0.5 + 8, find f(x).

Question shown in the answer section as a hyperlinked link.

How does integration by parts work ad when to use it?