Integration Method of substitution or change of variable

Method of substitution or change of variable

The method of substitution in integration is similar to finding the derivative of function of function in differentiation. By using a suitable substitution, the variable of integration is changed to new variable of integration which will be integrated in an easy manner.

The success of the above method depends on the selection of suitable substitution either x = φ(u) or u = g(x).

Note 11.2

The substitution for the variable of integration is in trigonometric function, use a rough diagram to find the re -substitution value for it. Suppose the variable of integration x is substituted as x = tanθ . After integration suppose the solution is sec θ + cosecθ

For example, if x = tanθ, then from the figure