Find the volume of revolution about the x-axis of the curve y=1/sqrt(x^2+2x+2) for 0<x<1
The volume of revolution is given by integrating Piy2 dx from 0 to 1.Squaring, y2=1/(x2+2x+2)Completing the square, we see that y=1/((x+1)2+1)Make the substitution u=x+1, so du=dx. When x is 0, respectively 1, u is 1, respectively 2. So the volume is the integral of Pi/(u2+1) du from 1 to 2. This is Piarctan(u) evaluated from 1 to 2, which is Pi*(arctan(2)-arctan(1)). In a calculator, we see this is roughly 1.011 and this is the desired volume.
HG
Answered by Harry G. • Further Mathematics tutor
3490 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Express sin(5theta) in terms of sin(theta) and powers of sin(theta) only.
A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0. Find dy/dx and d^2y/dx^2. Verify that C has a stationary point when x = 4
A spring with a spring constant k is connected to the ceiling. First a weight of mass m is connected to the spring. Deduce the new equilibrium position of the spring, find its equation of motion and hence deduce its frequency f.
How do I express complex numbers in the form reiθ?