# Homework Help: Definite integral problem

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1. Mar 24, 2015

### Aceix

1. The problem statement, all variables and given/known data
integrate from 1 to 2 x(x^2-3)^(1/2) with respect to x.

2. Relevant equations

3. The attempt at a solution
i attempted using numerical approximations but at x=1, the function is not defined so is there a way to combine improper integrals with this?

Aceix.

2. Mar 24, 2015

### fourier jr

I read your problem as $$\int_{1}^{2} x\sqrt{x^{2} - 3}\,dx$$ & used the substitution $u = x^{2} - 3$ then $\frac{1}{2}du = x\,dx$ so it's no improper integral. I'm not sure why you say the function is not defined at x=1.

3. Mar 24, 2015

### Dick

It's not defined because at x=1 because 1-3 is negative and square root of a negative is not defined. You would have to properly define the square root as a complex number to be able to integrate.

4. Mar 24, 2015

### Aceix

So how do I define the square root as a complex number?

5. Mar 24, 2015

### fourier jr

argh sorry about that but I did notice that when I tried $\int^{2}_{1} \frac{x\,dx}{\sqrt{x^2 - 3}}$ just in case I misread the original post

6. Mar 24, 2015

### Dick

If $x^2-3$ is negative then the complex square roots are either $i \sqrt{3-x^2}$ or $-i \sqrt{3-x^2}$. You have to pick which one you want. This is called 'choosing a branch'. Why are you doing this problem?

7. Mar 24, 2015

### Aceix

Saw it in a book(preparing for an exam).

8. Mar 24, 2015

### Dick

The problem has two possible answers since you need to make a branch choice. If you aren't really doing complex numbers, then possibly i) they just expect you to say it's not defined or ii) it's a typo.

9. Mar 24, 2015

thanks!