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} (x2e4x) dx.
Using the integration by parts formula (below), one can yield an intermediary equation, namely V = pi*[e4/4-(1/2)int_{0}^{1} (xe4x)]. Application of the integration by parts formula again solves the second integral of xe4x, 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).
HS
Related Maths A Level answers
All answers ▸If y = 4x^3 - 6x^2 + 7 work out dy/dx for this expression
Express 3 cos θ + 4 sin θ in the form R cos(θ – α), where R and α are constants, R > 0 and 0 < α < 90°.
A curve C is defined by the parametric equations x=(4-e^(2-6t))/4 , y=e^(3t)/(3t), t doesnt = 0. Find the exact value of dy/dx at the point on C where t=2/3 .
How do you solve 3sin2AtanA=2 for 0<A<180?