INTEGRATION BY
SUBSTITUTION
So far we have dealt with functions, either directly integrable using
integration formula (or) integrable after decomposing the given
functions into sums & differences.
In these cases, using proper substitution, we shall reduce the given form into
standard form, which can be integrated using basic integration formula.
When the integrand (the function to be integrated) is either in
multiplication or in division form and if the derivative of one full or
meaningful part of the function is equal to the other function then the
integration can be evaluated using substitution method as given in the
following examples.
The above integration can be evaluated by taking y = log x.
,* Integrals of some standard forms:
same type and the use of substitution y = f(x) will reduce the
given function to simple standard form which can be integrated
using integration formulae.
, 2. WORKED EXAMPLES
PART – A
SUBSTITUTION
So far we have dealt with functions, either directly integrable using
integration formula (or) integrable after decomposing the given
functions into sums & differences.
In these cases, using proper substitution, we shall reduce the given form into
standard form, which can be integrated using basic integration formula.
When the integrand (the function to be integrated) is either in
multiplication or in division form and if the derivative of one full or
meaningful part of the function is equal to the other function then the
integration can be evaluated using substitution method as given in the
following examples.
The above integration can be evaluated by taking y = log x.
,* Integrals of some standard forms:
same type and the use of substitution y = f(x) will reduce the
given function to simple standard form which can be integrated
using integration formulae.
, 2. WORKED EXAMPLES
PART – A
