1. Let f be a function for which

exists. Which of the following expressions is equal to I with the order of integration reversed?

A

B

C

D

 

E

 

 

Solution: A

To see this, graph the domain of integration. It is the region bounded by the lines y = x, y = 2 x and the lines x = 2, x = 4. It is the region bounded by the four red lines below:

This region is split into two triangles by the black line. The lower one is defined by the inequalities

The upper one is defined by the inequalities

Thus double integral I splits into the two double integrals in A when the order of integration is reversed.