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Calculus Cheat Sheet Integrals

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Sandra Watson
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The Petroleum Institute

Integrals
Definitions

Definite Integral: Suppose f ( x) is continuous
on [a,b] . Divide [a,b] into n subintervals of
width D x and choose *
i x from each interval.

Fundamental Theorem of Calculus

Part I : If f ( x) is continuous on [a,b] then
( ) ( ) x
a
g x = ò f t dt is also continuous on [a,b]
and ( ) ( ) ( ) x
a
d
g x f t dt f x
dx
¢ = ò = .

Part II : f ( x) is continuous on[a,b] , F ( x) is
an anti-derivative of f ( x) (i.e. F ( x) = ò f ( x) dx )
then ( ) ( ) ( ) b
a
ò f x dx = F b – F a .

Standard Integration Techniques
Note that at many schools all but the Substitution Rule tend to be taught in a Calculus II class.

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Calculus Cheat Sheet Integrals

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