I was given the following question:
Compute the volume of the solid bounded by \(z=x^2\), \(z=x+2\), \(y+z=5\), and \(y=-1\)
This is what I found.
\( \int_{-1}^{2}\int_{x^2}^{x+2}\int_{-1}^{5-z}1\ dy\ dz\ dx=\frac{99}{5}\) (using a CAS)
I'm not so worried about the final answer - I am more nervous about my bounds. My bounds for \(y\) and \(z\) are self-explanatory. For \(x\) I set the two \(z\) equations equal and solved for \(x\). Is this correct?
Compute the volume of the solid bounded by \(z=x^2\), \(z=x+2\), \(y+z=5\), and \(y=-1\)
This is what I found.
\( \int_{-1}^{2}\int_{x^2}^{x+2}\int_{-1}^{5-z}1\ dy\ dz\ dx=\frac{99}{5}\) (using a CAS)
I'm not so worried about the final answer - I am more nervous about my bounds. My bounds for \(y\) and \(z\) are self-explanatory. For \(x\) I set the two \(z\) equations equal and solved for \(x\). Is this correct?
