# Definitive Integral any ideas

1. Aug 12, 2013

### Djokara

Any ideas how to solve this
$$\int_0^h {\frac{1}{\sqrt{1+(r({\frac{1}{z}}-{\frac{1}{h}}))^2}}}\,dz$$
Don't have an idea from where to begin

Last edited: Aug 12, 2013
2. Aug 12, 2013

### SteamKing

Staff Emeritus
The correct term is 'definite integral'.

Is r a constant?

3. Aug 12, 2013

### Djokara

Yeah, this is problem from ED R is radius and h is height of cone.

4. Aug 12, 2013

### LCKurtz

Start by simplifying the integrand.

5. Aug 12, 2013

### jackmell

$$\frac{1}{\sqrt{1+(r/z-a)^2}}$$

now, can you simplify that and get:

$$\frac{z}{\sqrt{Q(z)}}$$

where $Q(z)$ is a quadratic polynomial in z? Then we'd have:

$$\int \frac{z}{\sqrt{Q(z)}} dz$$

Now I don't know about you, but I'd look in my Calculus text book about integrands with radicals with quadratic expressions (I did). And what is the first thing done when that happens?

Last edited: Aug 12, 2013
6. Aug 12, 2013

### Djokara

That worked but solution is messy.