find volume by integrating cross sectional areas

To find volume of a solid, slice the solid into infinitely thin slices (cross-sections) and integrate the area of these slices.

$V={\int }_a^{b}A(x)dx$ (cross-section perpendicular to x-axis) $V={\int }_a^{b}A(y)dy$ (cross-section perpendicular to y-ayis)