What is an indefinite integral?

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Answer 1 · 2015-08-31T09:04:52

An indefinite integral of a function $f(x)$ is a family of functions $g(x)$ for which: $g'(x)=f(x)$

An indefinite integral of a function $f(x)$ is a family of functions $g(x)$ for which: $g'(x)=f(x)$ .

Examples:

1) if $f(x)=x^3$ , then indefinite integral is:

$int x^3dx=x^4/4+C$ , because:

$(x^4/4)'=4*x^3/4=x^3$ , and $C'=0$ for any real constant $C$

2) If $f(x)=cosx$ , then

$int cosx dx= sinx+C$ , because:

$(sinx)'=cosx$