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- the process of finding
the areas bounded by
curves, volumes of
various solids, center
of gravity and other
geometric and physical
applications.
Indefinite Integral


example:
1.


example:
2.


example:
3.

example:
example:
1.


example:
2.

example:
3.


example:
4.


example:
example:
1.


example:
2.


example:
3.


example:
1.


2.


3.


4.
5.




6.
7.


8.


9.


10.
Sine and
   Cosine
Functions
1.
           n≠ -1


           n= -1

example:
b.
2.
           n≠ -1


           n= -1

example:
a.
b.
3.         m is odd



example:
4.         m is odd



example:
example:
b.
5.         m and n are
              even




example:
a.
6.
 a.


example:
b.


example:
c.


 example:
Tangent and
     Secant
  Functions
1.         m and n are
              odd



example:
2.         n is even




example:
3.         m is even




example:
Cotangent
       and
  Cosecant
 Functions
1.         m and n are
              odd



example:
2.         n is even >2




example:
,
,
Definite Integral


example:
1. The integral of a
constant multiple of a
function is that same
constant     times     the
integral of the functions.


example:
2. The integral of the sum
of two functions is the
sum of their integrals.


 example:
3. The sign of an integral
changes when its limits
of             integration
interchanged.



example:
Integral calculus

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Integral calculus