Chapter 13.2, Problem 81E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a.    In the iterated integral ${\displaystyle {\int }_c^d{\displaystyle {\int }_a^{b}f\left(x,y\right)dxdy}}$, the limits a and b must be constants or functions of x.

b.    In the iterated integral, ${\displaystyle {\int }_c^d{\displaystyle {\int }_a^{b}f\left(x,y\right)dxdy}}$, the limits c and d must be functions of y.

 c.    Changing the order of integration gives ${\displaystyle {\int }_0^2{\displaystyle {\int }_1^{y}f\left(x,y\right)dxdy}}={\displaystyle {\int }_1^y{\displaystyle {\int }_0^{2}f\left(x,y\right)dydx}}$.