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
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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
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U-substitution
1
1
n
uduu
nn
Integral form of the chain rule (function times its derivative)
Where u is a function of x
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1) Find dxx3
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x form u form (Reverse Chain Rule)Power Rule:
Trig Rules:
Integration by Recognition
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2) Find dxxx62 3510
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3) Find dxx 2075
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4) Find dxxx 13cos 2
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Definite Integral Substitution
Perform a complete change of variablesIncluding the limits of integration
b
a
af
bf
nn duudxxf)(
)(
)]([
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5) Find
0
4
2 )(sec)tan(
dxxx
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6) If 0 < k < π then k when 2
1)2cos(
0
k
dxx
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7) find dx 16
3
02 x
x
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8) find 12
4
0 x
x
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9) find 253
0
2 dxxx
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10) Suppose f is a continuous function and
6
4
3
2
)( find 8 )2( dxxfdxxf
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HOME WORKU-substitution worksheet