Rules of integration

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Rules of integration
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klawdet
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Mar. 24, 2016
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Rules of integration
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Rules of integration
Rules of Integration Exponential and Trigonometric
Function
• … 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
Rules of Integration
in Exponential Function 1. 2. 3.
Remember the three
General rules for Integration 1. 2. 3.
Examples: 1. Integrate 2. Integrate
.
3. Integrate u-substitution u =
-x du = -1 dx -1 du = dx
Example: Integrate
Example: Integrate
Examples: Integrate
Examples: Integrate u-substitution u = 2x+3 du
= 2 dx (1/2) du = dx
Rules of Integration
in Trigonometric Function
Trigonometric Functions A. B. C. D. C. D. E. F. G. H. I.
Rules of Differentiation
Indefinite Integrals
Indefinite integrals result
from trigonometric identities and u-substitution
Examples A. Integrate u-substitution u =
3x du = 3dx (1/3) du = dx Recall
B. Integrate Examples u-substitution u =
5x du = 5dx (1/5) du = dx Recall
C. Integrate Examples u-substitution u
= 4x du = 4dx (1/4) du = dx Recall
D. Integrate Examples
Trigonometric Functions A. B. C. D. C. D. E. F. G. H. I.
D. Integrate Examples
Indefinite Integrals
D. Integrate Examples u-substitution u
= sin x du = cos x dx
Rules of Differentiation
D. Integrate Examples u-substitution u
= sin x du = cos x dx
E. Integrate Examples
Trigonometric Functions A. B. C. D. C. D. E. F. G. H. I.
E. Integrate Examples u-substitution u
= 10x du = 10dx (1/10)du = dx
F. Integrate Example u-substitution u =
sin x du = cos dx Recall
INTEGRATE THE FOLLOWING 1. u-substitution
u-substitution
Thank You and God Bless