Question

Triple integrals. Changing the limits of integration.

Answer 1

Change the limits of integration for the following triple integral

\[\int\limits_{0}^{2}\int\limits_{0}^{x^2}\int\limits_{0}^{x}f(x,y,z) dzdydx\]

Answer 2

Algebraically

Answer 3

@Zarkon

Answer 4

use the inequalities inside the integral

\[0\le x\le 2\]
\[0\le y\le x^2\]
\[0\le z\le x\]

Answer 5

I have written down the implied inequalities.

Answer 6

but I do not know where to go from there.

Answer 7

@Zarkon

Answer 8

probably better to write
\[0\le x\le 2\]
\[0\le y\le x^2\le 4\Rightarrow 0\le \sqrt{y}\le x\le 2\]
\[0\le z\le x\le 2\]

Answer 9

Now if I define \[0\le z \le2\]