Virtual University Course MTH101 - Calculus and Analytical Geometry Lecture No 25 Instructor's Name: Dr. Faisal Shah Khan Course Email: mth101@vu.edu.pk

1. 25- Integrations VU
Lecture No.25 Integrations
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Here the dark region is area under the curve
y=f(x) in the interval [a,b].
This process of finding A(x) is called
antidifferentiation problem. By simple guessing we
see that
If we agree that the area above a singe point
Should be taken as zero, then on putting A(0) = 0 ,
And x=0, we get C=0. So we can write

2. 25- Integrations VU
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Here to find the area under the curve, we have
to find a function A(x) whose derivative is f(x). i.e.
For simplicity, the dx is sometimes absorbed
into the integrand. For example
1dx∫ can be written as
dx∫
2
1
dx
x∫ can be written as
2
dx
x∫
Integration Formulas
Some basic integration formulas are;

3. 25- Integrations VU
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Example
Part (b) and (c) of theorem 5.2.3 can be
extend to more than two Functions, which in
combination with part (a) results in the following
General formula:

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