i ntergration and u-s ubstitution 4-a. basic integration rules remember derivatives and integrals...
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INTERGRATION AND U-SUBSTITUTION
4-A
Basic Integration Rules
Remember derivatives and integrals are inverse operations Hence: antiderivative
dxxf
dxxfb
a
)( integral indefinite
)( integral definite : Symbol
The definite integral can be thought of as the area between a and b and between the curve of f(x) and the x-axis
U-substitution
1
1
n
uduu
nn
Integral form of the chain rule (function times its derivative)
Where u is a function of x
1) Find dxx3
x form u form (Reverse Chain Rule)Power Rule:
Trig Rules:
Integration by Recognition
2) Find dxxx62 3510
3) Find dxx 2075
4) Find dxxx 13cos 2
Definite Integral Substitution
Perform a complete change of variablesIncluding the limits of integration
b
a
af
bf
nn duudxxf)(
)(
)]([
5) Find
0
4
2 )(sec)tan(
dxxx
6) If 0 < k < π then k when 2
1)2cos(
0
k
dxx
7) find dx 16
3
02 x
x
8) find 12
4
0 x
x
9) find 253
0
2 dxxx
10) Suppose f is a continuous function and
6
4
3
2
)( find 8 )2( dxxfdxxf
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