Area of y = 2 Sqrt x is rotated about the y axis with attempt

[Riazy]

Homework Statement

Hellow guys i am stuck at this problem, you can see how far I have done, could someone show me how I can complete the square of this problem and how it is integrated, thanks!



http://img98.imageshack.us/i/img0003lz.jpg/

Homework Equations

The Attempt at a Solution

http://img98.imageshack.us/i/img0003lz.jpg/

 

[Riazy]

Anyone? The information is presented on the uploaded jpg.

 

[LCKurtz]

Write
$$x^2+x = (x^2+x + 1/4)-1/4=\left(x+\frac 1 2\right)^2-\left(\frac 1 2\right)^2$$

Letting w = x + 1/2 gets it into the form

$$\sqrt{w^2-a^2}$$

Then try the substitution $w = a\cosh(t)$

 

[Riazy]

What is a in your case?

 

[LCKurtz]

What is a in your case?

You mean in your case. a = 1/2.