Why is the integral of x^(n-1) dx =x^(n)/n? How does integral of x^(n-1) dx turn to the integral of x^(n) dx? Thanks.

Question

Explain  each step. By Detail.Thanks.

Answer 1

Hi Ab.

 

Do you know how when you integrate  ∫x³ dx  you get  (x⁴)/4 + C

 

If you let n = 4, then  n - 1 = 3  

 

and we could rewrite the integral above as  ∫x^n-1 dx you get (xⁿ)/n + C

 

It is the integration of x^power that you are accustomed to, only this time it is all in letters instead of numbers.  It is the "backwards" of the power rule if you were taking the derivative.