This chapter is chiefly concerned with three techniques – i.e. evaluating repeated integrals, changing the order of integration in repeated integrals and changing variables in multiple integrals. The important feature of each technique is the necessity of ensuring that the correct limits of integration are used. This is fairly straightforward in the two variable cases provided one is not tempted to hurry things along by such short cuts as dispensing with a diagram.
The theoretical explanation of the formula for changing variables given in §11.3 should be omitted if this is found troublesome.
Techniques similar to those ...