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
3065 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸It is given that f(x)=(x^2 +9x)/((x-1)(x^2 +9)). (i) Express f(x) in partial fractions. (ii) Hence find the integral of f(x) with respect to x.
How do you plot a complex number in an Argand diagram?
Using the substitution u = ln(x), find the general solution of the differential equation y = x^2*(d^2(y)/dx^2) + x(dy/dx) + y = 0
A tank contains 500L of salty water. Pure water is pumped in at a rate of 10 L/sec, and the the mixture is pumped out at a rate of 15L/ sec. If the concentration of salt is 5g/L initially, form an equation of amount of salt, s, at t seconds.