What is an indefinite integral?

1 Answer
Aug 31, 2015

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

Explanation:

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#