calculus-integrals.pdf

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where and 
 
INTEGRATION BY SUBSTITUTION 
COMMON INTEGRALS 
 
 
 or 
 
INTEGRATION BY PARTS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
INTEGRATION PROPERTIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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EEWeb.com The Best Source for Electrical Engineering Resources EEWeb.com 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Left-hand and right-hand rectangle approximations 
Midpoint Rule 
Trapezoid Rule 
 
APPROXIMATING DEFINITE INTEGRALS 
 
 
 
 
APPROXIMATION BY SIMPSON RULE FOR EVEN N 
 
CALCULUS 
 
INTEGRALS 
 
 
 
 
 
 
 
 
 
 
 
 
EXPRESSION EVALUATION 
 
SUBSTITUTION 
 
IDENTITY USED 
 
EXPRESSION 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRIGNOMETRIC SUBSTITUTION 
DEFINITE INTEGRAL DEFINITION 
 
 
 
 
 
 
 
 
where 
 
 
 and 
FUNDAMENTAL THEOREM OF CALCULUS 
 
 
 
 
 
where f is continuous on [a,b] and