9.17 Change of Variables in Multiple Integrals
INTRODUCTION
In many instances it is either a matter of convenience or of necessity to make a substitution, or change of variable, in a definite integral 
in order to evaluate it. If f is continuous on [a, b], x = g(u) has a continuous derivative, and dx = g′(u) du, then
f(x) dx = 
f(g(u)) g′(u) du,(1)
where the u-limits of integration c and d are defined by a = g(c) and b = g(d). There are three things ...
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