Q. 8 - Calculus

Question

Explain why the formula for the integral of $x^k$does not

apply when $k=-1.$ What is the integral of $x^{-1}?$

Step-by-Step Solution

Answer

Integral of $x^k$does not apply when $k=-1$because integral $x^{-1}$of is undefined.

Step 1. Given information.

 The given expression whose integral need to be determine is $x^{-1}.$

Step 2. Explanation.

Integral of $x^{-1}.$

$\int x^k=\frac{1}{k+1}{x}^{k+1}+C$

Substitute $k=-1.$

$$\begin{gathered} \int x^{-1}=\frac{1}{-1+1}{x}^{-1+1}+C \\ =\frac{1}{0}{x}^0+C \end{gathered}$$

Since $\frac{1}{0}$ is undefined so integral of $x^k$does not apply when $k=-1$because integral of$x^{-1}$ is undefined.