Working rule for Evaluating Definite Integral with Suitable Substitution
Suppose we have to evaluate the integral
Differentiating, we get
dt = g'(x) dx(2) Now the new variable is t.
The upper limit b and the lower limit a are in terms of x. Change these limits to the new variable g(b) and g(a).(3) Write
and express
in terms of t.
with respect to t.
Find the value of the integral between the new limits g(a) and g(b).
This gives integral of
Example:
1. Evaluate the definite integral
.
Solution:
Put t = tan-1x or x = tan t


when x = 0
tan t = 0
when x = 1, tan t =1 





Solution:




