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

Question

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

Quizplus · Accepted Answer

The integral of $ ( 7 - x ) ^ { - 1 } $ is $ \ln | 7 - x | $, but since the derivative of $7 - x$ is $-1$, we must multiply by $-1$ to compensate, making $k = -1$.

Find the Value of K That Makes the Antidifferentiation Formula ∫(7−x)−1dx\int ( 7 - x ) ^ { - 1 } d x∫(7−x)−1dx

Find the Value of K That Makes the Antidifferentiation Formula $\int ( 7 - x ) ^ { - 1 } d x$