Mapping integration points and weights
To see that this is correct by inserting the
the value of \( x_i=-1 \) (the lower end of the interval \( [-1,1] \))
into the expression for \( \tilde{x}_i \). That gives \( \tilde{x}_i=0 \),
the lower end of the interval \( [0,\infty) \). For
\( x_i=1 \), we obtain \( \tilde{x}_i=\infty \). To check that the new
weights are correct, recall that the weights should correspond to the
derivative of the mesh points. Try to convince yourself that the
above expression fulfills this condition.