Find region bounded by $z=1-x^2,\ z=x^2-1,\ y+z=1,$ and $y=0$ This question seemed simple to me what I did was the following:
when plotting the x-z graph I find two parabolas creating a leaf-shaped image and $1-x^2 \leq z \leq x^2-1$ and I find that $-1 \leq x \leq 1$ when plotting the y-z graph I find that $0 \leq y \leq 1-z$ thus I derive the following integral:
$$\int_{-1}^1\int_{1-x^2}^{x^2-1}\int_0^{1-z}1dydzdx$$
when I evaluate this, I get a negative value!!
Is my analysis as to how to carry this problem out incorrect?