text: # Area of Surface of Revolution
  
  1. Aug 3, 2009
  
  ### TheLegace
  
  1. The problem statement, all variables and given/known data
  Find area of surface generated by revolving about x-axis.
  
  y=x^3/3 1<=x<=sqrt(7)
  
  2. Relevant equations
  find f'(x) = x^2
  
  3. The attempt at a solution
  
  A = integral[ (x^3/3) * [(1+(x^2)^2] ^(1/2) ] ]dx
  = integral[ (x^3/3) * [(1+x^4) ^(1/2) ]dx
  I just don't know where to go from here.
  
  Any help is appreciated,
  Thank You.
  
  2. Aug 3, 2009
  
  ### Staff: Mentor
  
  Ordinary substitution: let u = 1 + x^4.
  
  I'm assuming that you have the correct integrand. If so, this substitution will help you out.
  
  3. Aug 3, 2009
  
  ### nickmai123
  
  You forgot the $$2\pi$$ in your equation, but you probably have that on paper. Here's what the integral should look like.
  
  $$A=\frac{2\pi}{3}\int^{\sqrt{7}}_{1}{x^{3}\sqrt{1+x^{4}}dy$$
  
  4. Aug 3, 2009
  
  ### TheLegace
  
  Oh whoops, ok well having that in there, how could I continue this problem?
  
  EDIT: I see how this can be solved, substition method.
  
  Thank You.
  
  Last edited: Aug 3, 2009
  5. Aug 3, 2009
  
  ### nickmai123
  
  Do what Mark44 said to do.
  
  $$u=1+x^{4}$$
  
  $$du=4x^{3}dx$$
  
  Last edited: Aug 3, 2009
  6. Aug 3, 2009
  
  ### Staff: Mentor
  
  Make that du = 4x3dx
  
  7. Aug 3, 2009
  
  Haha oops.