# anti-derivative problem

• Nov 20th 2012, 08:43 AM
kingsolomonsgrave
anti-derivative problem
I have f(x)= $\frac{8}{x^3}-\frac{7}{x^7}$ and I want to find F(x)

I am also given that F(1)=0

I get F(x)= $\frac{7}{6x^6}-\frac{4}{x^2}+C$

and since F(1)=0

F(x)= $\frac{7}{6*(1)^6}-\frac{4}{(1)^2}+C=0$

F(x)= $\frac{7}{6}-4+C=0$

F(x)= $-17/6+C=0$

so c=17/6

however the above is wrong somewhere. I just don't see where
• Nov 20th 2012, 08:54 AM
skeeter
Re: anti-derivative problem
looks fine to me ...

$F(x) = \frac{7}{6x^6} - \frac{4}{x^2} + \frac{17}{6}$

$F(1) = \frac{7}{6} - \frac{24}{6} + \frac{17}{6} = 0$

$F'(x) = \frac{8}{x^3} - \frac{7}{x^7}$
• Nov 20th 2012, 08:55 AM
kingsolomonsgrave
Re: anti-derivative problem
hmmm, thanks! i was entering the answer into an online test, so it could be something i entered wrong (typo) or the online system has a bug.
• Nov 20th 2012, 04:44 PM
EveryStepTom
Re: anti-derivative problem
Hi-

I Thought some might benefit from seeing all the steps to this problem:

Given:

f ' (x) = 8 / x^3 - 7 / x^7 Where f(1)=0

Rewrite:

f ' (x) = 8*x^(-3) - 7*x^(-7)

Integrate:

8*x^(-3+1) 7*x^(-7+1)
= ∫ -------------- - ---------------
(-3+1) (-7+1)

= 8*x^(-2)/(-2) - 7*x^(-6)/(-6)

= -4*x^(-2) + (7/6)*x^(-6) + C

f (x) = -4 / x^2 + 7 / 6*x^6 + C

At f (1) = 0

f (1) = -4 / (1)^2 + 7 / 6*(1)^6 + C = 0

= -4 + 7/6 + C = 0

Common Denominator:

= -24 / 6 + 7 / 6 + C = 0

= -17 / 6 + C = 0

C = 17 / 6