Question

I need help with an integral.

Answer 1

which

Answer 2

\[ \begin{array}l\color{red}{\text{I}}\color{orange}{\text{n}}\color{#e6e600}{\text{t}}\color{green}{\text{e}}\color{blue}{\text{g}}\color{purple}{\text{r}}\color{purple}{\text{a}}\color{red}{\text{t}}\color{orange}{\text{i}}\color{#e6e600}{\text{o}}\color{green}{\text{n}}\color{blue}{\text{ }}\color{purple}{\text{n}}\color{purple}{\text{e}}\color{red}{\text{e}}\color{orange}{\text{d}}\color{#e6e600}{\text{s}}\color{green}{\text{ }}\color{blue}{\text{n}}\color{purple}{\text{o}}\color{purple}{\text{ }}\color{red}{\text{h}}\color{orange}{\text{e}}\color{#e6e600}{\text{l}}\color{green}{\text{p}}\color{blue}{\text{ }}\color{purple}{\text{.}}\color{purple}{\text{.}}\color{red}{\text{.}}\color{orange}{\text{.}}\color{#e6e600}{\text{ }}\color{green}{\text{✌}}\color{blue}{\text{}}\end{array} \]

Answer 3

\[V=\int\limits_{?}^{?}f(x,y,z)dV\]
\[f(x,y,z)=xy , x,y \ge , x^2+y^2+z^2\le1\]

Answer 4

Somehow I felt sphere and used the jacobi-determinant to rewrite the integral and to get V=4/3 * pi but to rewrite it I used a z component which f does not have so I am kind of clueless.

Answer 5

\[f(x,y,z)=xy\]
\[x,y \ge0\]
\[x^2+y^2+z^2\]

Answer 6

\[x^2+y^2+z^2 \le 1\]

Answer 7

Those are the conditions I have.

Answer 8

well, it does appear to be an 4th a sphere then