# Stuck on taking the integral of

1. Aug 2, 2004

### carlchen

from 0 to 3, ( 1 + [ 1/2x^(1/2) - 1/2x^(-1/2) ]^2 )^(1/2) dx

I started to foil the ^2 term and then tryed to use the u sub, but It doesn't seem to work out. this problem is killing me!!!

2. Aug 2, 2004

### HallsofIvy

Staff Emeritus
Try that again! ((1/2)x1/2- (1/2)x-1/2)1/2=
(1/4)x- 1/2+ (1/4)x-1.

Now, when you add 1 to that you get (1/4)x+ 1/2+ (1/4)x-1. In other words, exactly the same thing except with +1/2 instead of -1/2!

Now that = (what?)2.

3. Aug 2, 2004

### Zurtex

I think HallsofIvy is saying mess about with the algebra. I did and in a few steps got:

$$\frac{1}{2} \int_0^3 x^{\frac{1}{2}} + x^{-\frac{1}{2}} dx$$

But I am not 100% confident on my skills so don't just copy that down.

4. Aug 2, 2004

### e(ho0n3

Another proof that you need to be good at algebra in order to be good at calculus.

5. Aug 2, 2004

### HallsofIvy

Staff Emeritus
And you have to be good at calculus to be good at differential equations- and you have to be good at differential equations to be good at analysis, It just keeps going!!