rules of integration
TRANSCRIPT
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Rules of IntegrationExponential and Trigonometric
Function
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• ... finding an Integral is the reverse of finding a Derivative.
• (So you should really know about Derivatives )• Like here:• Example: What is an integral of 2x?
• We know that the derivative of x2 is 2x ...
• ... so an integral of 2x is x2
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Rules of Integration in Exponential Function
1.
2.
3.
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Remember the three General rules for Integration
1.
2.
3.
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Examples:
1. Integrate
2. Integrate .
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3. Integrate
u-substitution u = -x du = -1 dx-1 du = dx
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Example:
Integrate
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Example: Integrate
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Examples:
Integrate
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Examples:
Integrateu-substitution u = 2x+3 du = 2 dx(1/2) du = dx
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Rules of Integration in Trigonometric Function
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Trigonometric Functions
A.
B.
C.
D.
C.
D.
E.
F.
G.
H.
I.
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Rules of Differentiation
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Indefinite Integrals
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Indefinite integrals result from trigonometric identities and u-
substitution
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Examples
A. Integrate
u-substitution
u = 3x
du = 3dx
(1/3) du = dx
Recall
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B. Integrate
Examples
u-substitution
u = 5x
du = 5dx
(1/5) du = dx
Recall
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C. Integrate
Examples u-substitution
u = 4x
du = 4dx
(1/4) du = dx
Recall
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D. Integrate
Examples
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Trigonometric Functions
A.
B.
C.
D.
C.
D.
E.
F.
G.
H.
I.
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D. Integrate
Examples
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Indefinite Integrals
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D. Integrate
Examplesu-substitution
u = sin x
du = cos x dx
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Rules of Differentiation
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D. Integrate
Examplesu-substitution
u = sin x
du = cos x dx
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E. Integrate
Examples
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Trigonometric Functions
A.
B.
C.
D.
C.
D.
E.
F.
G.
H.
I.
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E. Integrate
Examples u-substitution
u = 10x
du = 10dx
(1/10)du = dx
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F. Integrate Example
u-substitution
u = sin x
du = cos dx
Recall
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INTEGRATE THE FOLLOWING1.
u-substitution u-substitution
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Thank You and
God Bless