BCH3 - CH 3 - Integration ● ● ● The Fundamental Thm...

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Unformatted text preview: CH 3 - Integration ● ● ● The Fundamental Thm of Calculus ● Techniques of Integration ● Applications The computation of 1 . Indefinite Integrals ☺ F ( x ) — ( differentiation ) → F´ ( x ) = f ( x ) ☻ Reverse procedure !!! Let F & f be 2 functions defined on an interval I . F is called an antiderivative of f on I if F´ ( x ) = f ( x ) for all x in I . The indefinite integral of f wrt x = f ( x ) dx = the set of all antiderivatives of f If F´ ( x ) = G´ ( x ) for all x in I , then there exists C s.t. G ( x ) = F ( x ) + C for all x in I. If F is an antiderivative of f on I , then F + C is also an antiderivative of f on I , & every antiderivative of f on I is of this form. Thus, f ( x ) dx = F ( x ) + C Integral sign Integrand Constant of integration Geometrical Interpretation • The process on integration is to find all curves y = F ( x ) + C s.t. their slopes at x are f ( x )....
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This note was uploaded on 05/10/2011 for the course MATH 1505 taught by Professor Yap during the Winter '11 term at National University of Singapore.

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BCH3 - CH 3 - Integration ● ● ● The Fundamental Thm...

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