10
\includegraphics[max width=\textwidth, alt={}, center]{96cc217a-ffb3-4764-946e-e32271784ad7-4_764_929_255_609}
The diagram shows the line \(y = x + 1\) and the curve \(y = \sqrt { } ( x + 1 )\), meeting at \(( - 1,0 )\) and \(( 0,1 )\).
- Find the area of the shaded region.
- Find the volume obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(\boldsymbol { y }\)-axis.