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#