1. ## Antiderivative

Determine the antiderivative for $f'(x)=\frac{1-20}{x^3}$, $f(1)=20$

2. Originally Posted by XIII13Thirteen
Determine the antiderivative for $f'(x)=\frac{1-20}{x^3}$, $f(1)=20$
Are you sure? What's the point of the numerator?

3. Hello,

Erm...
Are you sure of 1-20 ?

By the way, this is easy, because the antiderivative of $\frac{1}{x^3}=x^{-3}$ is $-\frac{1}{2} x^{-2} +C = \frac{-1}{2x^2} +C$

With C to be found with the indication f(1)=20

4. ## Here is what you do

Originally Posted by XIII13Thirteen
Determine the antiderivative for $f'(x)=\frac{1-20}{x^3}$, $f(1)=20$
you have $\int{\frac{-19}{x^3}dx}=\frac{19}{2x^2}+C$and you know that $f(1)=20$...so $\frac{19}{2(1)^2}+C=20$...solve for C and you have your original function

5. It's $\frac{-19}{x^3}$ ^^