Iterated Integrals

Definition

• With $R=[a,b]\times [c,d]$ as a rectangle
• With $f$ integrable over Region $R$ A cut perpendicular to $x$ axis is:

$$\int {\int }_{R}f(x,y)dA={\int }_a^b[{\int }_c^{d}f(x,y)dy]dx$$

A cut perpendicular to $y$ axis is:

$$\int {\int }_{R}f(x,y)dA={\int }_c^d[{\int }_a^{b}f(x,y)dx]dy$$