Video Transcript
Determine the indefinite
integral of negative two over seven multiplied by 𝑥 to the power of negative
nine with respect to 𝑥.
In our integral, we simply have
a power function. So we can use the power rule
for integration in order to find this integral. It tells us that the indefinite
integral of 𝑥 to the power of 𝑛 with respect to 𝑥 is equal to 𝑥 to the power
of 𝑛 plus one over 𝑛 plus one plus 𝐶. In our case, we’re integrating
negative two-sevenths 𝑥 to the power of negative nine with respect to 𝑥. So our power of 𝑥 is negative
nine. We can start by writing down
our constant which is negative two-sevenths.
Then since our value of 𝑛 is
negative nine, we next need to write 𝑥 to the power of 𝑛 plus one over 𝑛 plus
one. So that’s 𝑥 to the power of
negative nine plus one which is 𝑥 to the power of negative eight over negative
nine plus one. So that’s negative eight. Then we mustn’t forget to add
our constant of integration 𝐶. For our final step here, we
just need to simplify. And we obtain our solution
which is that the indefinite integral of negative two-seventh multiplied by 𝑥
to the power of negative nine with respect to 𝑥 is equal to 𝑥 to the power of
negative eight over 28 plus 𝐶.
