- #1

- 4

- 0

## Homework Statement

[itex]\int^{1}_{0}\int^{x^2}_{0}\int^{y}_{0} f(x,y,z) dz dy dx[/itex]

Find 5 equivalent iterated integrals.

## Homework Equations

[itex]0 ≤ z ≤ y[/itex]

[itex]0 ≤ y ≤ x^2[/itex]

[itex]0 ≤ x ≤ 1[/itex]

## The Attempt at a Solution

1) [itex]\int^{1}_{0}\int^{√y}_{0}\int^{x^2}_{0} f(x,y,z) dz dx dy[/itex]

I will try dz dy dx first.

Because y = x^2, so [itex]0 ≤ z ≤ x^2[/itex]

Because y = x^2, so [itex]0 ≤ x ≤ √y[/itex]

And by the same logic, [itex]0 ≤ y ≤ 1[/itex]

When I integrate for f(x,y,z) = 1, the correct answer is 1/10. I do not get the same answer with my solution. Help! Is it possible to solve this without graphing it? Or is it necessary to get the correct answer?