Find the volume of the solid enclosed by the parabolic cylinder $y=x^2$ and the planes $z = 3 + y$ and $z= 4y$ by subtracting two volumes.
$$\text{Volume} = \int_a^b\int_c^d \text{?}\,dy \, dx - \int_a^b\int_c^d \text{?}\, dy \ dx$$
I have a hard time imagining how those planes extend over the x-axis... they're like both on x axis right? do they superimpose, or ... how it's gonna look like? Does anyone have 3d plotting software? Can you plot the two planes, and the parabolic cylinder on a 3d graph?
I tried to sketch, but it just looks awful :(
