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Title: Primitive and indefinite integral
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Primitive and indefinite integral
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Primitive and indefinite integral
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The function F(x) is called
primitive for the function f(x),
if
F (x) f (x)
...
'
2
Obviously, for the same
function
2
f (x) x
primitive is also
3
x
F( x )
C,
3
where C is an arbitrary
constant
...
elongated ”S”from “Summa”
argument
differential
In this way:
f
(
x
)
dx
F
(
x
)
C
...
A geometrically indefinite
integral is a family of “parallel”
curves:
y
y F( x) C2
y F(x)
o
x
y F( x) C1
Every function continuous on the
segment (a; b) has a primitive on
this interval and, therefore, an
indefinite integral
...
Title: Primitive and indefinite integral
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Primitive and indefinite integral
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Primitive and indefinite integral