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Mathematics
Calculus
Difference between integral and antiderivative?
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[QUOTE="Ssnow, post: 5448570, member: 555040"] Algebraically the antiderivative is the ''inverse'' of a derivation. Let ##f(x)## a continuous function, we say that ##F(x)## is an antiderivative (or primitive) of ##f## if ##F'(x)=f(x)## (assuming that ##F## has derivative). As example is ##f(x)=x## then an antiderivative is ##F(x)=\frac{x^{2}}{2}## because ## F'(x)=x=f(x)##. We observe that when you find an antiderivative ##F(x)## you have infinity antiderivatives because also ##F(x)+c## (where ##c## is a constant ex 2,3,...) is, in fact ##(F(x)+c)'=F'(x)=f(x)##. The family of functions ##F(x)+c## is also called the integral of ##f(x)## respect ##x## and yhe usual notation is ##\int f(x)dx=F(x)+c##. [/QUOTE]
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Forums
Mathematics
Calculus
Difference between integral and antiderivative?
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