I'm new to triple integral and this triple integral volume problem seems impossible to solve, and I have no idea where to start and how to solve it, could someone have a look at it please.
Let $G$ be the wedge in the first octant that is cut from the cylindrical solid $y^2 + z^2 < 1$ by the planes $y = x$ and $x = 0$. Evaluate $\iiint_G dV$
Best Answer
$$\int_0^1\int_0^{\sqrt{1-z^2}}\int_0^ydxdydz=\int_0^1\int_0^{\sqrt{1-z^2}}ydydz=\int_0^1\frac{(1-z^2)}{2}dz=\left[\frac z2\right]_0^1-\left[\frac{z^3}6\right]_0^1=\frac12-\frac16=\frac13$$