Question

find all the antiderivatives for the following function f(y)=-\frac{12}{y^{13}} the antiderivatives of f(y)=-\frac{12}{y^{13}} are f(y)=

Explanation:

Step1: Rewrite the function

Rewrite $f(y)=-\frac{12}{y^{13}}$ as $f(y)= - 12y^{-13}$.

Step2: Apply power - rule for antiderivatives

The power - rule for antiderivatives is $\int y^{n}dy=\frac{y^{n + 1}}{n+1}+C$ ($n
eq - 1$). Here $n=-13$, so $\int(-12y^{-13})dy=-12\int y^{-13}dy$.

Step3: Calculate the antiderivative

$-12\times\frac{y^{-13 + 1}}{-13 + 1}+C=-12\times\frac{y^{-12}}{-12}+C$.

Step4: Simplify the result

$y^{-12}+C=\frac{1}{y^{12}}+C$.

Answer:

$\frac{1}{y^{12}}+C$