# Another Triple Integral Check

1. Jul 8, 2011

### iamalexalright

1. The problem statement, all variables and given/known data
Evaluate triple integral of 3xy over the bounded region:

$$y = x^{2}$$
$$x = y^{2}$$
$$z = 6x + y$$

3. The attempt at a solution
Bounds on integral would be:
$$0 \leq x \leq 1$$
$$x^{2} \leq y \leq \sqrt{x}$$
$$0 \leq z \leq 6x + y$$

Correct?

2. Jul 8, 2011

### Dick

If they also gave you the bound z>=0 that looks fine. Otherwise the region isn't bounded.

3. Jul 8, 2011

### iamalexalright

Yep, z = 0 included

I get 9/8. Btw, what do you use to calculate them ?

4. Jul 8, 2011

### Dick

I use a software package called Maxima to actually do the integrals. I use my head to get the limits. What do you use? And I do get 9/8. We seem to be getting lucky here. I've usually made a mistake by now.

5. Jul 8, 2011

### iamalexalright

Just started using wolframalpha.com for the integrals. Just wanted to make sure my syntax and what not was correct.

Have to draw it out to get the limits heh

6. Jul 8, 2011

### Dick

You must be doing it right. Sure, the integration part is mechanical, no reason not to use a calculator there. The head work is the hard part and you seem to be getting it right.