Virtual University Course MTH101 - Calculus and Analytical Geometry Lecture No 31 Instructor's Name: Dr. Faisal Shah Khan Course Email: mth101@vu.edu.pk

1. 31-Evaluating Definite Integral by Substitution VU
Lecture No. 31
Evaluating Definite Integral by Substitution
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1
There are two different methods to evaluate definite
integral by Substitution. In first method we first evaluate
the integral and then put the limits. Where as in second
method, when we substitute some function, then we also
change the limit of the integral with respect to new
substitution. Here are given two methods, one can
choose any one of following method.
( )
2 32
0
1Evaluate x x dx+∫

2. 31-Evaluating Definite Integral by Substitution VU
© Copyright Virtual University of Pakistan
2
2
2
lim ,
0 0 1 1
2 2 1 5
To change the it
When x u
When x u
= ⇒ = + =
= ⇒ = + =
2
1u x= +
Here we first substitute and change limit and
then evaluate the integral.
Numerical Approximation of Definite
Integral
Recall that the Riemann Sum
, which we use to approximate the area under the
Curve. This expression is an approximation to
Original area, unless we take limit .
In practice, where we do not take this limit, it cannot
Be evaluated exactly. Thus we take the following
approximation.
( )*
1
n
k k
k
f x x
=
∑ V
n → +∞