Find the value of k that makes the antidifferentiation formula true.
-$\int x ^ { - 7 } d x$ = k $x ^ { - 6 }$ + C
A) 6
B) -6
C) $\frac { 1 } { 6 }$
D) - $\frac { 1 } { 6 }$

Question

Find the value of k that makes the antidifferentiation formula true. 
-$\int x ^ { - 7 } d x$ = k $x ^ { - 6 }$ + C
A) 6
B) -6
C) $\frac { 1 } { 6 }$
D) - $\frac { 1 } { 6 }$

Quizplus · Accepted Answer

The general formula for antidifferentiation of $x^n$ is $\frac{x^{n+1}}{n+1}$ for $n \neq -1$. Applying this to $x^{-7}$, we get $\frac{x^{-6}}{-6}$, which simplifies to $-\frac{1}{6}x^{-6}$. Therefore, $k = -\frac{1}{6}$.

Find the Value of K That Makes the Antidifferentiation Formula ∫x−7dx\int x ^ { - 7 } d x∫x−7dx

Find the Value of K That Makes the Antidifferentiation Formula $\int x ^ { - 7 } d x$