CHANGE OF VARIABLE OF INTEGRATION
If a determination of f(x) dx is not immediately obvious in terms of elementary functions, useful
results may be obtained by changing the variable from x to t according to the transformation x = gً)t).
(This change of integrand that follows is suggested by the differential relation dx = g("t( dt.) The fundamental
theorem enabling us to do this is summarized in the statement
f )x) dx = f (gt)g(t)" dt
where after obtaining the indefinite integral on the right we replace t by its value in terms of x, i.e.,
t = g(ًx)ق. This result is analogous to the chain rule for differentiation .
The corresponding theorem for definite integrals