Graph of the triangular region with edges on the points
and
The leftmost point of the triangular region begins at the
-axis at point
and linearly increases until the point
The equation of the line between the points
and
is given as
The region contains the entire area to the right of the line
and to the left of the vertical line
Coming up from the
-axis, the graph contains an arbitrarily chosen value on the
-axis, labeled
which is between
and
The graph showcases the distance between the point labeled
and the axis of rotation which is
The distance between these two
values is given as the function
which will give us the radius of the cylindrical shell once the solid is formed by rotating about the
-axis. Additionally, coming up from the line
is a red horizontal line, which meets the right side of the triangular region, which is given by the vertical line
This vertical line is labeled
and will give the us the height of the cylindrical shells.