Virtual University Course MTH101 - Calculus and Analytical Geometry Lecture No 29 Instructor's Name: Dr. Faisal Shah Khan Course Email: mth101@vu.edu.pk

1. 29- Definite Integral VU
Lecture No. 29 Definite Integral
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Recall that in the previous lecture we divide the
area under the curve in rectangles with equal width.
And then taking limit , to approximate the area. But
As in the following figure if keep on dividing the
Left hand side rectangles, and when we take the
Limit on width approaches to zero, the larger rec-
tangle remains as it is. And we cannot approxi-
mate the area well. For this
For example, if we make partition of interval
[0,6], then we may have this form,

2. 29- Definite Integral VU
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The numbers b and a are called the upper and
lower limit of integrations.
Evaluate the definite integral
Evaluate the definite integral

3. 29- Definite Integral VU
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3
( ) ( ) ( )
( )
( ) ( ) ( )
( ) ( )
5 5 5
1 3 3
3
1
3 5 3
1 1 5
5 5
1 3
1, 3,
1 3
4
f x dx f x dx f x dx
Find f x dx
By Above theorem we can write
f x dx f x dx f x dx
f x dx f x dx
= − =
= +
= −
= − −
= −
∫ ∫ ∫
∫
∫ ∫ ∫
∫ ∫