# Thread: Finding F(x) (INTEGRAL)

1. ## Finding F(x) (INTEGRAL)

Consider the function .
Let be the antiderivative of with .
Then ?

I don't understand what it's asking. Do I simply find the antiderivative?

2. Originally Posted by Archduke01
Consider the function .
Let be the antiderivative of with .
Then ?

I don't understand what it's asking. Do I simply find the antiderivative?
Yes, $F(x)$ is the antiderivative of $f(x)$.

And then you use the boundary condition to evaluate the integration constant.

3. I'm doing something wrong. I get $-6 x^{-2} /2 + 2 x^{-6} /6$.

Procedure; .

I separated the 6 and 2, then brought the denominators up getting $6 \int x^{-3} - 2 \int x^{-7}$. Do I apply the power rule at this point?

4. Originally Posted by Archduke01
I'm doing something wrong. I get $-6 x^{-2} /2 + 2 x^{-6} /6$.

Procedure; .

I separated the 6 and 2, then brought the denominators up getting $6 \int x^{-3} - 2 \int x^{-7}$. Do I apply the power rule at this point?
Your writing of integrals needs work. You can't leave off the $dx$'s.

It should read $6\int{x^{-3}\,dx} - 2\int{x^{-7}\,dx}$.

But yes, now apply the power rule.

5. I did apply the power rule, and the original answer is the answer I got. It's not correct though.

6. Originally Posted by Prove It
Your writing of integrals needs work. You can't leave off the $dx$'s.

It should read $6\int{x^{-3}\,dx} - 2\int{x^{-7}\,dx}$.

But yes, now apply the power rule.
$6\int{x^{-3}\,dx} - 2\int{x^{-7}\,dx} = 6\left(-\frac{1}{2}x^{-2}\right) - 2\left(-\frac{1}{6}x^{-6}\right) + C$

$= -\frac{3}{x^2} - \frac{1}{3x^6} + C$.