Volumes of Cross Sections

Finding a volume from a function that a dimension of a cross section and the geometric formula relating area to that dimension

Steps

1. Sketch a picture
2. Determine how the shapes are stacked (horizontal → $dx$, vertical → $dy$)
3. Write a formula for the base in terms of x or y
4. Write a general equation or area of each cross section in terms of x or y
5. Sum all the areas using $V={\int }_a^{b}A(x)dx$ or $V={\int }_a^{b}A(y)dy$