Evaluation of Definite Integral by Substitution
Category : JEE Main & Advanced
When the variable in a definite integral is changed, the substitutions in terms of new variable should be effected at three places.
(i) In the integrand (ii)In the differential i.e., \[dx\] (iii) In the limits
For example, if we put \[\varphi (x)=t\] in the integral \[\int_{a}^{b}{f\{\varphi (x)\}\varphi '(x)dx}\], then \[\int_{a}^{b}{f\{\varphi (x)\}\varphi '(x)dx=\int_{\varphi (a)}^{\varphi (b)}{f(t)\,dt}}\].
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