Triple Integral Evaluation for Bounded Region with Polynomial Boundaries

[iamalexalright]

Homework Statement

Evaluate triple integral of 3xy over the bounded region:

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

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?

 

[Dick]

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

 

[iamalexalright]

Yep, z = 0 included

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

 

[Dick]

Yep, z = 0 included

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

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.

 

[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

 

[Dick]

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

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.