Chapter 15.2, Problem 2CFU

To determine

To find: The reason for that the power rule for anti derivative is not valid when $n=-1$ .

Answer to Problem 2CFU

The power rule is not applicable for anti derivatives when $n=-1$ .

Explanation of Solution

Calculation:

Using the power rule of anti derivatives,

  $f\left(x\right)=x^n$ ,where is a rational number other than $-1$ , the anti derivative is $F\left(x\right)=\frac{x^{n+1}}{n+1}+C$ .

So, here the power rule is not valid when $n=-1$ , because if we take $n=-1$ .

  $F\left(x\right)=\frac{1}{0}$

That is the denominator of $F\left(x\right)$ will be zero which gives absurd value for the antiderivative.

So, the power rule is not applicable for anti derivatives when $n=-1$ .

Therefore, the power rule is not applicable for anti derivatives when $n=-1$ .