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
3045 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Prove by induction that 6^n + 4 is divisible by 5 for all integers n >= 1
Prove by induction that the sum from r=1 to n of (2r-1) is equal to n^2.
A curve has equation y=(2-x)(1+x)+3, A line passes through the point (2,3) and the curve at a point with x coordinate 2+h. Find the gradient of the line. Then use that answer to find the gradient of the curve at (2,3), stating the value of the gradient
Solve the following complex equation: '(a + b)(2 + i) = b + 1 + (10 + 2a)i' to find values for 'a' and 'b'