find the surface $D = \{(x, y) \mid x^{3} \le y, 1 \le xy, x + y \le 10\}$

Question

My task is to find the surface of the area $D = \left\{ (x, y) \mid x^{3} \leq y, 1 \leq xy, x + y \leq 10 \right\} $.

$$x: \begin{cases} & x \leq \sqrt[3]{y} \\ & x \geq \frac{1}{y}\\ & x \leq 10 - y \end{cases}$$

Then, I'm not sure what to do. Can you give me some advice? I have to solve it with double integrals.

Answer 1

Which area do you want to calculate?
The upper right area is closed, the lower left is not.
You could specify additional restrictions $x\ge 0$ or $y\ge 0$.
See also